STATIS multivariate three-way method for evaluating quality of life after corneal surgery: Methodology and case study in Costa Rica

Francisco J. Perdomo-Argüello; Estelina Ortega-Gómez; Purificación Galindo-Villardón; Víctor Leiva; Purificación Vicente-Galindo; Francisco J. Perdomo-Argüello; Estelina Ortega-Gómez; Purificación Galindo-Villardón; Víctor Leiva; Purificación Vicente-Galindo

doi:10.3934/mbe.2023264

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 4: 6110-6133. doi: 10.3934/mbe.2023264

Previous Article Next Article

Research article Special Issues

STATIS multivariate three-way method for evaluating quality of life after corneal surgery: Methodology and case study in Costa Rica

1.
Facultad de Medicina, Universidad de Iberoamérica, San José, Costa Rica
2.
Departamento de Estadística, Universidad de Panamá, Panama City, Panama
3.
Departamento de Estadística, Universidad de Salamanca, Salamanca, Spain
4.
Centro de Estudios e Investigaciones Estadísticas, ESPOL, Guayaquil, Ecuador
5.
Centro de Gestión de Estudios Estadísticos, Universidad Estatal de Milagro, Guayas, Ecuador
6.
Escuela de Ingeniería Industrial, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

Received: 03 October 2022 Revised: 15 December 2022 Accepted: 18 December 2022 Published: 31 January 2023

Vision-related quality of life (QoL) analyzes the visual function concerning individual well-being based on activity and social participation. Because QoL is a multivariate construct, a multivariate statistical method must be used to analyze this construct. In this paper, we present a methodology based on STATIS multivariate three-way methods to assess the real change in vision-related QoL for myopic patients by comparing their conditions before and after corneal surgery. We conduct a case study in Costa Rica to detect the outcomes of patients referred for myopia that underwent refractive surgery. We consider a descriptive, observational and prospective study. We utilize the NEI VFQ-25 instrument to measure the vision-related QoL in five different stages over three months. After applying this instrument/questionnaire, a statistically significant difference was detected between the perceived QoL levels. In addition, strong correlations were identified with highly similar structures ranging from 0.857 to 0.940. The application of the dual STATIS method found the non-existence of reconceptualization in myopic patients, but a statistically significant recalibration was identified. Furthermore, a real change was observed in all patients after surgery. This finding has not been stated previously due to the limitations of the existing statistical tools. We demonstrated that dual STATIS is a multivariate method capable of evaluating vision-related QoL data and detecting changes in recalibration and reconceptualization.

Keywords:

Citation: Francisco J. Perdomo-Argüello, Estelina Ortega-Gómez, Purificación Galindo-Villardón, Víctor Leiva, Purificación Vicente-Galindo. STATIS multivariate three-way method for evaluating quality of life after corneal surgery: Methodology and case study in Costa Rica[J]. Mathematical Biosciences and Engineering, 2023, 20(4): 6110-6133. doi: 10.3934/mbe.2023264

Related Papers:

[1]	Yilei Tang, Dongmei Xiao, Weinian Zhang, Di Zhu . Dynamics of epidemic models with asymptomatic infection and seasonal succession. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1407-1424. doi: 10.3934/mbe.2017073
[2]	Ayako Suzuki, Hiroshi Nishiura . Seasonal transmission dynamics of varicella in Japan: The role of temperature and school holidays. Mathematical Biosciences and Engineering, 2023, 20(2): 4069-4081. doi: 10.3934/mbe.2023190
[3]	Kazunori Sato . Basic reproduction number of SEIRS model on regular lattice. Mathematical Biosciences and Engineering, 2019, 16(6): 6708-6727. doi: 10.3934/mbe.2019335
[4]	Zhenguo Bai . Threshold dynamics of a periodic SIR model with delay in an infected compartment. Mathematical Biosciences and Engineering, 2015, 12(3): 555-564. doi: 10.3934/mbe.2015.12.555
[5]	Steady Mushayabasa, Drew Posny, Jin Wang . Modeling the intrinsic dynamics of foot-and-mouth disease. Mathematical Biosciences and Engineering, 2016, 13(2): 425-442. doi: 10.3934/mbe.2015010
[6]	Abdelheq Mezouaghi, Salih Djillali, Anwar Zeb, Kottakkaran Sooppy Nisar . Global proprieties of a delayed epidemic model with partial susceptible protection. Mathematical Biosciences and Engineering, 2022, 19(1): 209-224. doi: 10.3934/mbe.2022011
[7]	John E. Franke, Abdul-Aziz Yakubu . Periodically forced discrete-time SIS epidemic model with disease induced mortality. Mathematical Biosciences and Engineering, 2011, 8(2): 385-408. doi: 10.3934/mbe.2011.8.385
[8]	Islam A. Moneim, David Greenhalgh . Use Of A Periodic Vaccination Strategy To Control The Spread Of Epidemics With Seasonally Varying Contact Rate. Mathematical Biosciences and Engineering, 2005, 2(3): 591-611. doi: 10.3934/mbe.2005.2.591
[9]	Hai-Feng Huo, Qian Yang, Hong Xiang . Dynamics of an edge-based SEIR model for sexually transmitted diseases. Mathematical Biosciences and Engineering, 2020, 17(1): 669-699. doi: 10.3934/mbe.2020035
[10]	Xinli Hu . Threshold dynamics for a Tuberculosis model with seasonality. Mathematical Biosciences and Engineering, 2012, 9(1): 111-122. doi: 10.3934/mbe.2012.9.111

Abstract

1. Introduction

In a knowledge-based economy, intellectual capital (IC) is considered an important resource for firms' value creation, growth and innovative capacity (Chen et al., 2005; Dzenopoljac et al., 2017; Lev, 2004; Lev and Sougiannis, 1996; Liu and Wong, 2011; Xu and Wang, 2018, 2019). The financial crisis, beginning at the end of 2007, accentuated the scarcity of financial resources as well as the difficulty in accessing funds for investment in intangible assets, namely IC investments (Cincera et al., 2015; Hall et al., 2016). IC investments, without physical or financial form and often referred to as intangible assets, generate future benefits (Lev, 2004) and contribute greatly to value creation through employee knowledge, organizational processes, and innovation (Serenko and Bontis, 2004; Wang et al., 2014). Moreover, IC investments represent an investment in intangible assets and are, often, complementary to tangible investments. However, firms face obstacles in accessing external sources of financing to fund intangible asset investments (Liu and Wong, 2011; Ferrando and Preuss, 2018; Lim et al., 2020).

IC is composed of several components and depending on their nature, namely, when they are not identifiable, they cannot serve as collateral in accessing credit, conversely, tangible assets can serve as collateral, and, therefore, firms with a high level of IC investments faced more obstacles in obtaining finance with favourable terms (Liu and Wong, 2011). Aboody and Lev (2000) argue that information asymmetry between firm insiders and outsiders is more pronounced in firms with a high level of IC investment. IC assets present lower liquidation value due to their inherent liquidity risk. The specificity of IC assets may create adverse selection, moral hazard and opportunistic behaviour in managers (Aboody and Lev, 2000; Brown et al., 2009). These problems may influence intangible-intensive firms' financing decisions (Lev, 2005; Liu and Wong, 2011; Ferrando and Preuss, 2018). In fact, the information opacity associated with intangible assets generates problems of information asymmetry, which is pointed out as one of the reasons why firms with high levels of intangible assets tend to rely on internal funds to fund innovative projects (Carpenter and Petersen, 2002; Hall and Lerner, 2010; Magri, 2014).

In accordance with Myers (1984) and Myers and Majluf (1984), the problems of asymmetric information are greater for firms with a high level of intangible assets due to the specificity of this type of assets, which increases the costs of debt and equity issues. Gatchev et al. (2009) and Hogan and Hutson (2005) conclude that high-tech firms, characterized by high levels of intangible investments, prefer to rely more on equity issues than on debt. These findings reverse the predictions of Pecking Order Theory (POT, henceforth) regarding firms' financing choices.

According to Carpenter and Petersen (2002), the returns of high technology investments are biased, subject to high uncertainty and have a high probability of failure. These factors imply that high-tech firms are strongly affected by capital market imperfections. High-tech firms invest heavily in R & D, which has little collateral value, and so capital market imperfections may impact more strongly on high-tech firms than on firms in other industries (Carpenter and Petersen, 2002). In this way, capital market imperfections may imply debt costs above those of equity issues, given that this last finance source does not require collateral and does not increase the financial risk. Furthermore, when high-tech firms provide detailed, useful information to investors about the sources of firm value creation, information asymmetry diminishes, and thus the cost of equity issues is reduced, and investors' decision-making process is improved (Cronje and Moolman, 2013; Dumay, 2016; Lal Bhasin, 2012; Osinski et al., 2017).

Firms in which R & D and technological innovation assume a prominent role, i.e. high-tech firms, should place greater emphasis on nurturing their intellectual capital. Considering, firstly, that high-tech firms have a fundamental role in providing knowledge for economic growth, and secondly, that these firms seem to face the consequences of capital market imperfections due to the high level of investment in intangible assets, namely IC investment, the current paper seeks to analyse the relationships between IC investment and high-tech firms' financing choices. Moreover, various empirical studies (Saleh et al., 2009; Bohdanovich and Urbanek, 2013; Bohdanovich, 2014) investigated the possible relationship between ownership structure and IC efficiency, providing evidence of a negative effect of insider ownership on IC. Therefore, this paper also analyses the relationship between the IC investment of high-tech firms and ownership concentration.

We consider internal finance, debt and equity issues as potential finance sources used by high-tech firms to fund IC investments. The research sample is composed of non-financial listed high-tech firms in 14 Western European countries for the period between 2004 and 2015. Like Moncada-Paternò-Castello (2016), who followed the European Commission (2006–2014) and OECD (1997) approach, we consider a sample of high-tech firms, in an attempt to capture the relationships between IC and financing sources in this type of firm.

The results suggest that internal finance and equity issues are positively, but debt is negatively related to IC assets in high-tech firms. The findings also suggest that in high-tech firms, ownership concentration impacts negatively on IC investment, suggesting that greater ownership concentration allows more efficient management of financial resources to match the needs for funding investments, namely IC investment. Concerning the impact of the financial crisis of 2008–2009, the results show a negative effect on IC investment.

Our study makes several contributions to the literature. To our knowledge, this is the first study exploring the relationships between finance sources and investment in IC in high-tech firms. In order to obtain a wide perspective of firms' financing choices, we use internal finance, debt and equity issues as financing sources, allowing us to analyse if these firms reverse the predictions of POT in their financing choices. Finally, our findings also contribute to the literature by analysing the impact of ownership concentration on IC investments.

The current paper is structured as follows. In Section 2, we present the theoretical framework and hypothesis formulation; Section 3 presents the methodology; in Section 4, we present the results; the results are discussed in Section 5; and finally, we conclude in Section 6.

2. Intellectual capital and high-techs firms' financing choices

In this study, we consider IC as the knowledge-based activities and processes that contribute to firms' innovation, value creation, competitive advantages and future benefits by adding value for stakeholders (Sardo and Serrasqueiro, 2018). IC assets, without physical or financial form, and often referred to as intangible assets, generate future benefits (Lev, 2004) and greatly contribute to value creation through employee knowledge, organizational processes, and innovation (Serenko and Bontis, 2004; Wang et al., 2014). IC can be decomposed in three components which are widely accepted among researchers (Edvinsson and Malone, 1997; Sydler et al., 2014; Sardo and Serrasqueiro, 2017; Sardo and Serrasqueiro, 2018), i.e., human capital (HC), structural (or organizational) capital (SC), and relational (or customer) capital (RC). Therefore, IC comprises employee knowledge, organizational processes, innovation capabilities, research and development projects, brand and relationships (Serenko and Bontis, 2004; Wang et al., 2014).

The strong embodiment of intangibles increases the sunk costs generated by firms' IC investments (Lev and Zambon, 2003). Firms with high levels of IC may face higher human costs due to the cost of salaries paid to highly trained human resources, such as scientists and engineers (Berk et al., 2010; Porter and Ketels, 2003). Potential earnings will be lost if trained human resources are dismissed or leave the firm.

In accordance with the predictions of pecking order theory (POT, hereafter) (Myers, 1984; Myers and Majluf, 1984), firms prefer internal finance, because it prevents exposure to an information asymmetry problem and is the cheapest source of capital to fund firm activities (Magri, 2014). When internal finance is exhausted, firms rely on external debt, and as a last option, they issue equity. This hierarchical order in the choice of finance sources is explained by the existence of asymmetric information, which may lead to adverse selection problems (Stiglitz and Weiss, 1981), increasing the costs of issuing equity. Some studies conclude that firms with greater asymmetric problems face greater adverse selection problems, and hence, worse conditions when obtaining credit. This adversity in obtaining credit can be diminished if firms possess tangible assets as collateral. Therefore, since firms obtain credit with lower costs than the costs of issuing equity, after internal finance is exhausted, they rely on debt, and issue equity as a last option.

Campello and Giambona (2013) and Qiu and La (2010) find that the redeployability of tangible assets increases borrowing capacity because it allows lenders to recover the credit in the case of borrower bankruptcy. When a firm has assets with lower liquidation values, creditors will establish a high premium risk, which increases the cost of debt. Consequently, firms with activities based on specific assets, such as IC assets, will face difficulties in accessing to credit, therefore they issue equity (Bah and Dumontier, 2001; Hall and Lerner, 2009; Wang and Tornhill, 2010).

Various authors (Carpenter and Petersen, 2002; Hall and Lerner, 2010; Magri, 2014; Myers, 1984; Myers and Majluf, 1984) conclude that high-tech firms prefer internal finance to fund their innovative activities due to the risk associated with such activities. For high-tech firms, several studies show a reverted POT, given that when internal finance is exhausted, these firms prefer to rely on external equity. Intangible assets, such as IC assets, are specific and non-redeployable, and have a low liquidation value, which increases bankruptcy costs and implies a low credit capacity for firms with activities based on such assets (Williamson, 1988). The firms with higher levels of intangible assets should fund their investment in intangible assets, firstly, through internal finance, which allows reduced transaction costs and avoids opportunistic behaviour by managers (Williamson, 1988; Močnik, 2001; Vilasuso and Minkler, 2001).

Prior empirical evidence (Hovakimian et al., 2001; MacKie-Mason, 1990; Titman and Wessels, 1988) showed a negative relationship between firms' intangible assets and leverage. Moreover, studies such as Gatchev et al. (2009), Hogan and Hutson (2005), Magri (2014), Blass and Yosha (2003) and Brown and Petersen (2009) found that high-tech firms prefer external equity to debt. In fact, Carpenter and Petersen (2002) argue that the uncertainty about the returns associated with high-tech investments prevents a high level of debt to avoid negative expectations from investors. Additionally, the problems of adverse selection in credit markets seem to be more acute for high-tech firms, and so lenders can use credit rationing instead of increasing interest rates (Carpenter and Petersen, 2002). Marginal bankruptcy costs may increase quickly for higher levels of debt in high-tech firms, whose activities are based on intangible assets that generate valuable growth opportunities but lose value when firms find themselves in financial distress (Carpenter and Petersen, 2002). In addition, innovative firms face problems of asymmetric information, and therefore, when internal finance is exhausted, this type of firm may choose to fund their activities by issuing equity rather than debt (Gatchev et al., 2009; Hogan and Hutson, 2005; Magri, 2014).

High-tech firms are intensive innovative firms with high level of intangible assets that may influence financing choices. In accordance with Aghion et al. (2004) there are three approaches of the capital structure theory that can explain the financing choices of innovative firms. In accordance with those authors, the approach based on bankruptcy costs argues that costs of bankruptcy are higher for innovative firms with a higher level of intangible assets. According to these authors, for a given level of debt, innovative firms face higher risk of bankruptcy. Consequently, this type of firms should present low level of debt to minimize the bankruptcy costs. Capital structure theory presents another approach based on agency costs and informational asymmetries between firm insiders and outsiders. For this approach, the innovative firms face asymmetric information; thus, equity issues may be a particularly expensive source of finance for these firms. (Aghion et al. 2004). According to Myers and Majluf (1984) firms with activities based on intangible assets are likely to prefer debt instead of equity issues to avoid dilution costs that actual shareholder face would face when firms issue external equity. The last approach of capital structure theory is an alternative to the pecking order theory that suggests that innovative firms may favour new equity rather than debt among these external sources. This is explained by innovative firms facing a lack of tangible assets that can be pledged as collateral, which constrains the access to credit in favourable terms. Therefore, innovative firms choose new equity finance instead of debt for funding their investment in intangible assets.

Various empirical papers (Saleh et al., 2009; Bohdanovich and Urbanek, 2013; Bohdanovich, 2014) investigated a supposed association of ownership structure with IC efficiency, providing evidence of a negative effect of insider ownership on IC measured by the VAIC index (Pulic, 2000). Saleh et al. (2009) studied 264 listed companies in Malaysia during the period 2005–2007 to determine whether there is a relationship between the VAIC, the different forms of ownership structures and profitability. Those authors found a negative and almost always statistically significant relationship between the VAIC, its components and family ownership. They concluded that the negative relationship would increase the likelihood of the opportunistic behavior of family members to the detriment of minority shareholders. Bohdanowicz and Urbanek (2013) investigated a sample of 354 Polish companies listed during the period 2006–2011 for a total of 1505 firm-year observations. The results show a negative and significant relationship between the VAIC and manager ownership Celenza and Rossi (2013) identify a relationship between VAIC and OC that is positive but almost not statistically significant.

Considering the previous arguments, in the current study, we argue that high tech firms which activities are based on intangible assets prefer internal finance and equity issue, avoiding debt for funding IC assets. Additionally, we argue that ownership concentration has a negative relationship with high-tech firms IC.

3. Data, variables and method

3.1. Database

Based on 14 Western European countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, Spain, Sweden and the United Kingdom (UK)) for the period between 2004 and 2015, our data were obtained for 821 non-financial, listed, high-tech firms.

A firm is defined as "High-Tech" if its main activity is one of the following: Chemicals, Machinery, Computers, Electrical Machinery, TV-Radio, Medical Equipment, Means of Transport. The data set was gathered from the DataStream database by Thomson Reuters. Therefore, it has an unbalanced panel structure, where the number of years a firm is present in the research sample varies between 3 and 12.

In order to mitigate potential survival bias, Guariglia (2008), Bond et al. (2003) and Cummins et al. (2006) in their studies allow firms' entry and exit is allowed, and using an unbalanced panel partially mitigates potential selection and survivor bias. Following those authors, in the current study firms' entry and exit from the research sample and using an unbalanced panel data allow to control the problem of selection and survival bias. The data was trimmed at one percent tails in order to control for the potential effects of outliers, which may derive from particular events, such as large mergers, errors in coding or firms' extraordinary shocks (Guariglia, 2008).

3.2. Estimation method and variable measurement

This study analyses the relationship between IC and financing choices in high-tech firms resorting to a static panel data model, i.e., pooled OLS, random effects and fixed effects, and a dynamic panel data model, i.e., GMM system (1998).

3.2.1. Static panel data model

This study uses a pooled OLS to estimate the following model:

${VAIC}_{i, t} = {\propto }_{0}+{\beta }_{1}{CF}_{i, t-1}+{\beta }_{2}{TDEBT}_{i, t-1}+{\beta }_{3}{EqIssue}_{i, t-1}{+ \beta }_{4}{OWNCONC}_{i, t-1}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +{\beta }_{5}{AGE}_{i, t-1}+{\beta }_{6}{SIZE}_{i, t-1}+{\beta }_{7}{Dcrisis}_{08;09}+ {e_{i,t}}$

(1)

The definition and measurement of the variables of in the Equation (1) are presented in Table 1.

Table 1. Variables and measurement.

Variables	Measurement
Dependent variables
Intellectual Capital investment ( ${VAIC}_{i, t}$ )	${VAIC}_{i, t}$ is the value added intellectual coefficient in the current period (VAIC^TM) corresponding to the sum of HCE plus SCE plus CEE, where: HCE is human capital efficiency (HCE) = value added (VA)/human capital (HC); SCE structural capital efficiency (SCE) = structural capital (SC)/value added (VA); and CEE is capital employed efficiency = value added (VA)/capital employed (CE), where VA is given by sales—operational expenses except employee costs.
Intangible Assets investment $({InvIntangible}_{i, t}$ )	Ratio between Intangible Assets in the current period and Total Assets in the current period.
Independent variables
$Cash\ Flow{(CF}_{i, t})$	Ratio of income plus depreciations and amortization to total assets in the current period.
Total Debt ${\mathrm{ }(TDEBT}_{i, t }$ )	Ratio of total debt in the current period to total assets in the current period.
Equity issue ( ${EqIssue}_{i, t }$ )	Ratio of net equity issues in the current period to total assets in the current period.
Ownership concentration ${ (OWNCONC}_{i, t}$ )	Variable NOSHEM (source: Datastream database) that aggregates the percentage of holdings of 5% or more by employees or family members.
Control variables
Size ${(SIZE}_{i, t}$ )	Natural logarithm of total assets in the current period.
${\mathrm{A}\mathrm{g}\mathrm{e} (AGE}_{i, t}$ )	Natural logarithm of the number of years of the firm's existence in the current period.
Financial Crisis ( ${Dcrisis}_{08;09}$ )	Dummy variable representing the financial crisis for the years 2008 and 2009.

| Show Table

DownLoad: CSV

The dependent variable used is ${VAIC}_{i, t}$ as a proxy for IC. The independent variables: ${CF}_{i, t-1}$ is cash flow in the previous period, ${TDEBT}_{i, t-1}$ is total debt in the previous period; ${EqIssue}_{i, t-1 }$ is net equity issues in the previous period; ${OWNCONC}_{i, t-1}$ is ownership concentration in the previous period. The control variables are: ${SIZE}_{i, t-1}$ is size in the previous period; ${AGE}_{i, t-1}$ is firm age in the previous period; and ${Dcrisis}_{08;09}$ is a dummy representing the financial crisis for the years 2008 and 2009.

The pooled OLS does not allow control of firms' individual unobserved effects and therefore Bevan and Danbolt (2004) conclude on the existence of heterogeneity due to not taking into consideration the influence of these effects on the estimated parameters.

The use of fixed effects or random effects panel data allows control of the influence of firms' individual unobserved effects on the estimated parameters. Therefore, considering the unobserved individual effects, the following fixed effects and random effects panel data model is estimated:

${VAIC}_{i, t} = {\propto }_{0}+{\beta }_{1}{CF}_{i, t-1}+{\beta }_{2}{TDEBT}_{i, t-1}+{\beta }_{3}{EqIssue}_{i, t-1}{+ \beta }_{4}{OWNCONC}_{i, t-1}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +{\beta }_{5}{AGE}_{i, t-1}+{\beta }_{6}{SIZE}_{i, t-1}+{\beta }_{7}{Dcrisis}_{08;09}+{\rm{ \mathsf{ μ} }}_{i, t}$

(2)

in which: ${u_{i,t}} = {v_i} + {e_{i,t}}$ , $v_i$ are unobserved individual effects. The difference between a pooled OLS and a model that considers individual effects is that the latter takes into consideration the $v_i$ term. The remaining variables have a similar definition and measurement as those presented for Equation (1).

The Lagrange Multiplier (LM) test is used to verify the relevance of the individual effects. The null hypothesis is the non-relevance of unobservable individual effects, while the alternative hypothesis is the relevance of unobservable individual effects. Failing to reject the null hypothesis, it is possible to conclude that the unobservable individual effects are not relevant, and therefore, a pooled OLS is suitable to estimate the parameters of the explanatory variables used. Otherwise, it is concluded that a pooled OLS is not appropriate to estimate the parameters of the explanatory variables used in this study.

If there is no correlation between the unobservable individual effects and explanatory variables, the random effects panel data estimator is more suitable. Otherwise, a panel data model that considers the existence of fixed effects should be used. The Hausman test is used to test the existence of correlation between unobservable individual effects and explanatory variables, where the null hypothesis is the non-existence of that type of correlation, and the alternative hypothesis is the existence of correlation between unobservable individual effects and explanatory variables. If the null hypothesis is rejected, it is concluded that the correlation is relevant, and therefore a panel data estimator considering fixed effects should be used.

This study presents the most suitable panel data model according to the results of the LM and Hausman tests, consistent with the existence of first order autocorrelation.

3.2.2. Dynamic panel data model

Dynamic panel data models allow the use of time series data considering the heterogeneity in adjustment dynamics between different types of firms, due to the dynamic character of the main research variables studied. Therefore, we will use the Generalized Method of Moments (GMM), a dynamic estimator proposed by Blundell and Bond (1998), which allows us to control the endogeneity problem and avoids significant bias in estimates (Wooldridge, 2007). The efficiency of this estimator lies in the possibility of controlling correlation errors over time and heteroscedasticity across firms. The results of the GMM system (1998) estimator can only be valid on the following conditions: (1) validity of the restrictions created using instruments; and (2) there should be no second-order autocorrelation. To test the first condition, i.e., validity of the restrictions created by the instruments used, we use the Hansen test where the null hypothesis is validity of the restrictions created by the instruments used. For the second condition, we test for second-order autocorrelation, where the null hypothesis indicates there is no second-order autocorrelation. In the case of not rejecting the null hypothesis for the Hansen and second-order autocorrelation tests, we conclude that the GMM system (1998) estimator is valid and robust. By using a high number of instruments, the GMM system (1998) estimator leads to major improvements in efficiency compared with the first difference GMM estimator (Arellano and Bover, 1995; Blundell and Bond, 1998). Arellano and Bond (1991), Windmeijer (2005) and Roodman (2006) showed the reliability of the one-step GMM estimator, asymptotically more efficient than the two-step estimator due to the downward biased standard errors. In order to overcome this problem, Windmeijer (2005) developed the small sample corrector, which provides more accurate inference on the two-step procedure especially for the GMM system (1998) estimator (Roodman, 2009). Therefore, we used the two-step procedure with the correction proposed by Windmeijer (2005). To test validity of the instruments used, we resorted to the Hansen test.

GMM system (1998) dynamic estimator is used to estimate the following model:

${VAIC}_{i, t} = {\propto }_{0}+{\beta }_{1}{VAIC}_{i, t-1}+{\beta }_{2}{CF}_{i, t-1}+{\beta }_{3}{TDEBT}_{i, t-1}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ + {\beta }_{4}{EqIssue}_{i, t-1}{+ \beta }_{5}{OWNCONC}_{i, t-1}+{\beta }_{6}{AGE}_{i, t-1}+{\beta }_{7}{SIZE}_{i, t-1}\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +{\beta }_{8}{Dcrisis}_{08;09}+{\eta }_{i}+{\varepsilon }_{i, t}$

(3)

where: ${\eta }_{i}$ are non-observable individual effects and ${ \varepsilon }_{i, t}$ is the error term. The remaining variables have a similar definition and measurement to those presented for Equation (1).

4. Empirical results

4.1. Descriptive statistics and correlation matrix

Table 2 summarizes the descriptive statistics of the dependent and independent variables.

Table 2. Descriptive statistics.

Variables	N	Mean	Median	Standard Deviation
${VAIC}_{i, t}$	7474	2.1	2	1.1
${InvIntangible}_{i, t}$	9414	0.029	0.0045	0.33
${CF}_{i, t}$	9090	0.041	0.077	0.38
${TDEBT}_{i, t}$	9414	0.2	0.17	0.17
${EqIssue}_{i, t}$	8606	0.044	0	0.25
${OWNCONC}_{i, t}$	8813	17	0	23
${SIZE}_{i, t}$	9195	12	12	2.1
${AGE}_{i, t}$	9414	3.3	3.2	0.99
Note: Intellectual Capital investment ( ${\mathrm{V}\mathrm{A}\mathrm{I}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) $\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}\ \mathrm{ }\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w}{(\mathrm{ }\mathrm{C}\mathrm{F}}_{\mathrm{i}, \mathrm{t}})$ Total Debt ${\mathrm{ }(\mathrm{T}\mathrm{D}\mathrm{E}\mathrm{B}\mathrm{T}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Equity issue ( ${\mathrm{E}\mathrm{q}\mathrm{I}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{e}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Ownership concentration ${\mathrm{ }(\mathrm{O}\mathrm{W}\mathrm{N}\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) Size ${(\mathrm{S}\mathrm{I}\mathrm{Z}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) ${\mathrm{A}\mathrm{g}\mathrm{e}\mathrm{ }(\mathrm{A}\mathrm{G}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) Financial Crisis ( ${\mathrm{D}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{s}}_{08;09}$ ).

| Show Table

DownLoad: CSV

The results presented in Table 2 show that VAIC, the proxy of IC, presents an average of 2.1 and a standard deviation of 1.1, thus this variable does not present a considerable volatility. The average of cash flow is 0.041, the average of equity issues is 0.044 and the average of total leverage is 0.17. Considering that the standard deviation is superior to the average of cash flow and equity issues, we can conclude that these variables present some volatility. Additionally, firms, on average, present a size about €162754.8 thousand and on average, they are 27.1 years old. Regarding the variable ownership, it presents, on average, 17% that corresponds to the percentage of holdings of employees or family members.

The correlation matrix, presented in Table 3, shows the correlation and magnitude of the variables studied.

Table 3. Correlation matrix.

	${VAIC}_{i, t}$	${VAIC}_{i, t-1}$	${InvIntangible}_{i, t}$	${InvIntangible}_{i, t-1}$	${CF}_{i, t-1}$	${SIZE}_{i, t-1}$	${AGE}_{i, t-1}$	${EqIssue}_{i, t-1}$	${OWNCONC}_{i, t-1}$	${TDEBT}_{i, t-1}$
${VAIC}_{i, t}$	1.0000
${VAIC}_{i, t-1}$	0.6636*	1.0000
${InvIntangible}_{i, t}$	−0.0118	0.0112	1.0000
${InvIntangible}_{i, t-1}$	−0.0314	−0.0269	0.0725*	1.0000
${CF}_{i, t-1}$	0.2366*	0.2621*	0.0398*	−0.0015	1.0000
${SIZE}_{i, t-1}$	0.1164*	0.1342*	−0.0140	−0.0159	0.1476*	1.0000
${AGE}_{i, t-1}$	−0.1014 *	−0.0981*	0.0030	0.0060	0.0452*	0.2121*	1.0000
${EqIssue}_{i, t-1}$	−0.0309	−0.0206	−0.0033	−0.0167	−0.2037 *	−0.1327 *	−0.0678 *	1.0000
${OWNCONC}_{i, t-1}$	−0.0919 *	−0.0876*	−0.0308**	−0.0070	−0.0121	−0.2284 *	−0.0421 *	−0.0231	1.0000
${TDEBT}_{i, t-1}$	0.0124	0.0025	−0.0273	−0.0192	−0.1270 *	0.2649*	0.0413*	−0.0406*	−0.0242	1.0000
Note: Intellectual Capital investment ( ${\mathrm{V}\mathrm{A}\mathrm{I}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) $\mathrm{I}\mathrm{n}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{g}\mathrm{i}\mathrm{b}\mathrm{l}\mathrm{e}\ \mathrm{ }\mathrm{A}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{t}\mathrm{s}\ \mathrm{ }\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{m}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{ }\left({InvIntangible}_{i, t}\right)\mathrm{ }\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}\ \mathrm{ }\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w}{(\mathrm{ }\mathrm{C}\mathrm{F}}_{\mathrm{i}, \mathrm{t}})$ Total Debt ${\mathrm{ }(\mathrm{T}\mathrm{D}\mathrm{E}\mathrm{B}\mathrm{T}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Equity issue ( ${\mathrm{E}\mathrm{q}\mathrm{I}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{e}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Ownership concentration ${\mathrm{ }(\mathrm{O}\mathrm{W}\mathrm{N}\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) Size ${(\mathrm{S}\mathrm{I}\mathrm{Z}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) ${\mathrm{A}\mathrm{g}\mathrm{e}\mathrm{ }(\mathrm{A}\mathrm{G}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) Financial Crisis ( ${\mathrm{D}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{s}}_{08;09}$ ) 1. * significant at 1% level.

| Show Table

DownLoad: CSV

According to Gujarati and Porter (2010), problems of endogeneity between independent variables are relevant for correlation coefficients above 30%. There are no correlations above 30% among the independent variables.

The Lagrange Multiplier, LM (χ²), indicates a result of 101.53*** meaning that this result is statistically significant at 1% level and, therefore, we should reject the null hypothesis that the unobservable individual effects are not relevant in the explanation of the dependent variable. Therefore, the pooled OLS regression is not the most appropriate to estimate the results. Also, the Hausman test, Hausman (χ²), indicates a result of 58.99*** meaning that this result is statistically significant at 1% level and, therefore, we should reject the null hypothesis of the non-existence of correlation between unobservable individual effects and explanatory variables. Therefore, the fixed effects model is the most appropriate to use.

However, static models do not allow analysis of the dynamism of financial choices for IC investment. Therefore, this study uses the GMM system (1998) estimator, which besides the advantages already mentioned, considers the lagged dependent variable, ${VAIC}_{i, t-1}$ . Regarding the GMM system (1998) estimations, the Hansen (χ²) test is not statistically significant and, therefore, we cannot reject the null hypothesis of the validity of the instruments used. Moreover, the second-order autocorrelation tests, m2 (N(0, 1)), is not significant and, therefore, we do not reject the hypothesis of the non-existence of second-order autocorrelation for the estimated models. This being so, the results of the GMM system (1998) dynamic estimator are robust and can support discussion of the results. Therefore, in the following section we discuss the results obtained from using GMM system (1998) estimator.

4.2. GMM system results

The results of the estimated Equation (3) using the GMM system (1998) dynamic estimator are presented in Table 4.

Table 4. Estimation results—VAIC.

	Dependent Variable: ${\mathrm{V}\mathrm{A}\mathrm{I}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$
Independent Variables	Pooled OLS	RE	FE	GMM system (1998)
${VAIC}_{i, t-1}$				0.79409***
				(0.05057)
${CF}_{i, t-1}$	1.24073***	0.65381***	0.59755***	0.54851**
	(0.09124)	(0.09754)	(0.10917)	(0.19712)
${TDEBT}_{i, t-1}$	−0.84957***	−0.71144***	−0.44815***	−0.37700**
	(0.08530)	(0.11799)	(0.14769)	(0.13058)
${EqIssue}_{i, t-1}$	0.46048***	0.20930**	0.19777*	0.60002**
	(0.11118)	(0.10167)	(0.10760)	(0.21871)
${OWNCONC}_{i, t-1}$	−0.00047	−0.00076	−0.00088	−0.00145**
	(0.00057)	(0.00083)	(0.00103)	(0.00057)
${SIZE}_{i, t-1}$	0.02650***	0.00438	0.06989*	0.01597**
	(0.00752)	(0.01413)	(0.03688)	(0.00797)
${AGE}_{i, t-1}$	−0.08864***	−0.05423**	−0.10817	−0.09518**
	(0.01363)	(0.02721)	(0.06584)	(0.03868)
${Dcrisis}_{08;09}$	−0.10477***	−0.08876***	−0.07065**	−0.12865***
	(0.03350)	(0.02774)	(0.02849)	(0.02316)
CONS	2.15028***	2.35143***	2.67586***	0.62746***
	(0.09804)	(0.18117)	(0.45053)	(0.14663)
Observations	5,771	5,771	5,771	4,731
Firms	766	766	766	722
LM (χ²)		101.53***
Hausman (χ²)		28.94***
R²	0.06034	0.0557	0.01277
Wald (χ²)		114.39***
F (N(0, 1))	52.87***		9.238***	81.39***
Hansen (χ²)				61.27
m1 (N(0, 1))				−3.768***
m2 (N(0, 1))				2.170
Notes: Intellectual Capital investment ( ${\mathrm{V}\mathrm{A}\mathrm{I}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) $\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}\ \mathrm{ }\mathrm{F}\mathrm{l}\mathrm{o}\mathrm{w}{(\mathrm{ }\mathrm{C}\mathrm{F}}_{\mathrm{i}, \mathrm{t}})$ Total Debt ${\mathrm{ }(\mathrm{T}\mathrm{D}\mathrm{E}\mathrm{B}\mathrm{T}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Equity issue ( ${\mathrm{E}\mathrm{q}\mathrm{I}\mathrm{s}\mathrm{s}\mathrm{u}\mathrm{e}}_{\mathrm{i}, \mathrm{t}\mathrm{ }}$ ) Ownership concentration ${\mathrm{ }(\mathrm{O}\mathrm{W}\mathrm{N}\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{C}}_{\mathrm{i}, \mathrm{t}}$ ) Size ${(\mathrm{S}\mathrm{I}\mathrm{Z}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) ${\mathrm{A}\mathrm{g}\mathrm{e}\mathrm{ }(\mathrm{A}\mathrm{G}\mathrm{E}}_{\mathrm{i}, \mathrm{t}}$ ) Financial Crisis ( ${\mathrm{D}\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{s}}_{08;09}$ ) 1. CONS is the constant of the regressions. 2. Standard errors in parentheses. 3. *significant at 1% level, significant at 5% level and *significant at 10% level.

| Show Table

DownLoad: CSV

The results obtained for the relationships between the explanatory variables and ${VAIC}_{i, t}$ are the following: ${VAIC}_{i, t-1}, {CF}_{i, t-1}, {EqIssue}_{i, t-1}$ , and ${SIZE}_{i, t-1}$ have positive relationships with ${VAIC}_{i, t}$ ; while ${TDEBT}_{i, t-1}$ , ${OWNCONC}_{i, t-1}$ , ${AGE}_{i, t-1}, \mathrm{ }\mathrm{a}\mathrm{n}\mathrm{d}{Dcrisis}_{08;09}$ present negative relationships with ${VAIC}_{i, t}$ .

5. Discussion of the results

Regarding the estimations obtained using system GMM (1998) estimator, for the Equation (4):

${VAIC}_{i, t} = {\propto }_{0}+{\beta }_{1}{VAIC}_{i, t-1}+{\beta }_{2}{CF}_{i, t-1}+{\beta }_{3}{TDEBT}_{i, t-1}\\+ {\beta }_{4}{EqIssue}_{i, t-1}{+ \beta }_{5}{OWNCONC}_{i, t-1}+{\beta }_{6}{AGE}_{i, t-1}+{\beta }_{7}{SIZE}_{i, t-1}\\+ {\beta }_{8}{Dcrisis}_{08;09}+{\eta }_{i}+{\varepsilon }_{i, t}$

(4)

The results obtained for the relationships between the dependent variable ( ${VAIC}_{i, t}$ ) and the independent variables ${CF}_{i, t-1}$ , ${TDEBT}_{i, t-1}$ ${EqIssue}_{i, t-1}, {OWNCONC}_{i, t-1, }{AGE}_{i, t-1, }$ ${SIZE}_{i, t-1}$ , and ${Dcrisis}_{08;09}$ are presented in Table 4. Accordingly, the results suggest that cash flow (i.e., internal finance) and equity issues, in the previous period, present positive relationships with IC in the current period in high-tech firms. However, debt in the previous period has a negative impact on IC in the current period in high-tech firms. The results in Table 4 show that the impact of cash flow and equity issues is 0.55 and 0.6, respectively, while the effect of debt is about −0.38 on high-tech firms IC. These results evidence the positive effect of equity issues and internal finance, while debt has a negative impact of for high-tech firms IC. These results suggest that internal finance and equity issues are the financing choices preferred by high-tech firms to fund IC investment.

The results also suggest that high-tech firms tend to avoid resorting to debt to fund IC. Regarding the results obtained (Appendix A) for the relationships between investment in intangible assets and internal finance, debt and equity issues, it is possible to conclude they are like the results obtained for the relationships between IC and internal finance, debt and equity issues. This corroborates the argument of several authors (Frank and Goyal, 2008; Parsons and Titman, 2009) that firms with high levels of intangible assets tend to have less debt. Moreover, specific, non-redeployable assets, such as IC assets, hinder access to credit on favourable terms (Hall and Lerner, 2010; Magri, 2014), increasing credit costs. Therefore, the results suggest that high-tech firms rely on equity issues and internal finance to fund intangible assets, namely IC assets, to minimize the financial costs. In this context, Berk et al. (2010) identified a negative relationship between intellectual capital and leverage concluding that intellectual capital-intensive firms face greater indirect costs of bankruptcy due to the high costs associated with entrenched employee salaries. Those authors also conclude that firms with high levels of IC investment may face problems of asymmetric information due to the low liquidation value of IC assets. Therefore, these firms prefer internal funds and present lower levels of debt.

Furthermore, high-tech firms' use of internal finance is explained by lower costs, given that internal finance has no problems of asymmetric information. Issuing equity may be expensive due to transaction costs and problems of information asymmetry between firms' insiders and outsiders. However, Lee et al. (2014) state that high-tech investments are difficult to evaluate and involve high risk. Therefore, for these authors equity issues have many advantages over debt to fund high-tech investments, since they do not require collateral and do not increase the probability of firm bankruptcy. Furthermore, issuing equity gives shareholders greater control of managers' opportunistic behaviour. Additionally, several authors (Cronje and Moolman, 2013; Dumay, 2016; Lal Bhasin, 2012; Osinski et al., 2017) argue that when high-tech firms provide detailed, useful information to investors about the sources of firm value creation, information asymmetry diminishes, and thus the cost of equity issues is reduced, and investors' decision-making process is improved.

Thus, the current study seems to reverse the predictions of POT, given that high-tech firms seem to avoid using debt to fund their IC investments, relying on internal finance and equity issues. These results may be due to the problems of asymmetric information high-tech firms face with creditors and consequently poor terms in accessing credit. The results obtained here agree with various studies (Gatchev et al., 2009; Hogan and Hutson, 2005; Magri, 2014; Ferrando and Preuss, 2018). Furthermore, for firms in general, Bolek and Lyroud (2015) conclude that IC influences capital structure, equity issues being the main finance source of IC, while debt presents a negative relationship with IC. However, Lim et al. (2020) found a positive relationship between identifiable intangible assets and debt, but a negative impact of unidentifiable intangible assets on debt level. Liu and Wang (2011), using three patent-based variables as proxies for intellectual capital, found a positive relationship between capital intellectual and debt in high tech firms.

The results obtained provide empirical evidence of the influence of ownership concentration on high-tech firms' IC investments, given that the impact of ownership concentration on high-tech firms' IC investment is about −0.00145 (Table 4). In general, ownership concentration affects negatively IC investments in high-tech firms. This suggests that low ownership concentration brings benefits to the firm, as a more dispersed ownership structure seems to increase IC investment (Burkart et al., 1997; Prendergast, 2002).

Concerning the impact of the 2008–2009 crisis, the results show a negative effect on IC investment. This may be a consequence of the crisis adversely affecting the firm´s capacity to generate positive cash flows, consequently, firms became more dependent on external financing sources. However, during the financial crisis, most European firms faced credit constraints, therefore debt being a restriction as a funding source of investment.

6. Conclusion

This paper seeks to analyse the relationships between high tech firms' financing choices and IC investments. We use data collected from the DataStream database for a research sample of non-financial, listed, high-tech firms in 14 European countries referring to the period between 2004 and 2015.

The results suggest that high-tech firms fund IC investments through internal finance and equity issues. They also suggest that high-tech firms tend to avoid using debt to fund their innovative projects. These results suggest a modified version of pecking order theory. The problems of asymmetric information and agency probably imply unfavourable terms for high-tech firms in accessing to credit. Therefore, these firms choose equity issues and internal finance to fund IC assets. The results also suggest that low ownership concentration in high-tech firms brings benefits as a greater level of ownership concentration impacts negatively on IC investment.

Concerning the impact of the 2008–2009 crisis, there is a negative effect on IC investment, probably due to low capacity in generation internal finance due to the contraction of demand associated with the economic recession. Furthermore, the financial crisis impacted negatively on terms of credit, thus deteriorating the conditions for high-tech firms in accessing to credit to fund IC assets.

The current study presents several contributions. To our knowledge, this is the first study exploring the relationships between IC investment and high-tech firms' financing choices, showing the importance of internal finance and equity issues. Our findings also contribute to the literature by analysing the impact of ownership concentration on high-tech firms' IC investments.

Considering the potential positive impact of IC investments on firm innovative capacity, namely on processes and product development, we suggest managers to devote more attention to the contribution of IC to the generation of financial resources in the firm. For policy-makers, we suggest the need to develop programmes to promote firms' IC investment, since projects requiring relevant amount of capital invested in intangible assets may face obstacles in accessing to credit on favourable terms.

The current study has the following limitations. Countries' characteristics, such as legal aspects, or accounting practices, may influence the results. For future research, we suggest testing the impact of IC on financing choices by comparing results among different European countries. Also, in future research, we suggest the analysis of the relationship between corporate governance variables and IC investments.

Acknowledgments

The authors would like to express their acknowledge to the financial support of the research unit on Governance, Competitiveness and Public Policy—University of Aveiro, and CEFAGE-UBI—The Centre for Advanced Studies in Management and Economics of the University of Beira Interior, both sponsored by the FCT—Portuguese Foundation for the Development of Science and Technology, Ministry of Science, Technology and Higher Education and Science, project (UIDB/04058/2020) and project UIDB/04007/2020, respectively.

Conflict of interest

The authors declare no conflict of interest.

References

[1]	X. Zheng, Z. Li, X. Chun, X. Yang, K. Liu, A model-based method with geometric solutions for gaze correction in eye-tracking, Math. Biosci. Eng., 17 (2020), 33–74. https://doi.org/10.3934/mbe.2020071 doi: 10.3934/mbe.2020071
[2]	C. Zhao, C. Cai, Q. Ding, H. Dai, Efficacy and safety of atropine to control myopia progression: A systematic review and meta-analysis, BMC Ophthalmol., 20 (2020), 478. https://doi.org/10.1186/s12886-020-01746-w doi: 10.1186/s12886-020-01746-w
[3]	T. A. Althomali, Relative proportion of different types of refractive errors in subjects seeking laser vision correction, Open Ophthalmol. J., 12 (2018), 53–62. https://doi.org/10.2174/1874364101812010053 doi: 10.2174/1874364101812010053
[4]	World Health Organization, The impact of myopia and high myopia: Report of the Joint World Health Organization - Brien Holden Vision Institute Global Scientific Meeting on Myopia. University of New South Wales, Sydney, Australia, 2016.
[5]	S. L. Trokel, R. Srinivasan, B. Braren, Excimer laser surgery of the cornea, Am. J. Ophthalmol., 96 (1983), 710–715. https://doi.org/10.1016/S0002-9394(14)71911-7 doi: 10.1016/S0002-9394(14)71911-7
[6]	Y. Song, L. Fang, Q. Zhu, R. Du, B. Guo, J. Gong, et al., Biomechanical responses of the cornea after small incision lenticule extraction (SMILE) refractive surgery based on a finite element model of the human eye, Math. Biosci. Eng., 18 (2021), 4212–4225. https://doi.org/10.3934/mbe.2021211 doi: 10.3934/mbe.2021211
[7]	D. T. Azar, Refractive Surgery, Elsevier, USA, 2006. https://doi.org/10.1016/B978-0-323-03599-6.50059-6
[8]	World Health Organization, WHOQOL: Measuring quality of life, World Health Organization, Division of Mental Health and Prevention of Substance Abuse, Geneva, Switzerland, 1997. apps.who.int/iris/handle/10665/63482
[9]	A. Ahluwalia, L. L. Shen, L. V. Del Priore, Central geographic atrophy vs. neovascular age–related macular degeneration: Differences in longitudinal vision-related quality of life, Graefe's Arc. Clin. Exper. Ophthalmol., 259 (2021),, 259,307–316. https://doi.org/10.1007/s00417-020-04892-5
[10]	N. Li, X. J. Peng, Z. J. Fan, Progress of corneal collagen cross-linking combined with refractive surgery, Int. J. Ophthalmol., 7 (2014), 157.
[11]	P. J.Banerjee, V. R. Cornelius, Adjunctive intraocular and peri-ocular steroid (triamcinolone acetonide) versus standard treatment in eyes undergoing vitreoretinal surgery for open globe trauma (ASCOT): Study protocol for a phase Ⅲ, multi-centre, double-masked randomised controlled trial, Trials, 17 (2016), 339. https://doi.org/10.1186/s13063-016-1445-7 doi: 10.1186/s13063-016-1445-7
[12]	S. Feeny, A. Posso, L. McDonald, T. T. K. Chuyen, S. T. Tung, Beyond monetary benefits of restoring sight in Vietnam: Evaluating well-being gains from cataract surgery. PLoS One, 13 (2018), e0192774. https://doi.org/10.1371/journal.pone.0192774 doi: 10.1371/journal.pone.0192774
[13]	C. E. Schwartz, M. A. Sprangers, Methodological approaches for assessing response shift in longitudinal health-related quality-of-life research, Soc. Sci. Med., 48 (1999), e0192774. https://doi.org/10.1016/S0277-9536(99)00047-7 doi: 10.1016/S0277-9536(99)00047-7
[14]	M. Salmon, M. Blanchin, C. Rotonda, F. Guillemin, V. Sébille, Identifying patterns of adaptation in breast cancer patients with cancer‐related fatigue using response shift analyses at subgroup level. Cancer Med., 6 (2017), 2562–2575. https://doi.org/10.1002/cam4.1219 doi: 10.1002/cam4.1219
[15]	M. Friedrich, M. Zenger, A. Hinz, Response shift effects of quality of life assessments in breast cancer survivors, European J. Cancer Care, 28 (2019), e12979. https://doi.org/10.1111/ecc.12979 doi: 10.1111/ecc.12979
[16]	M. G.Verdam, F. J. Oort, M. A. Sprangers, Structural equation modeling–based effect-size indices were used to evaluate and interpret the impact of response shift effects, J. Clin. Epidemiol., 85 (2017), 37–44. https://doi.org/10.1016/j.jclinepi.2017.02.012 doi: 10.1016/j.jclinepi.2017.02.012
[17]	M. Preiß, M. Friedrich, J. U. Stolzenburg, M. Zenger, A. Hinz, Response shift effects in the assessment of urologic cancer patients' quality of life, European J. Cancer Care, 28 (2019), e13027. https://doi.org/10.1111/ecc.13027 doi: 10.1111/ecc.13027
[18]	T. Murata, Y. Suzukamo, T. Shiroiwa, N. Taira, K. Shimozuma, Y. Ohashi, et al., Response shift–adjusted treatment effect on health-related quality of life in a randomized controlled trial of taxane versus S-1 for metastatic breast cancer: Structural equation modeling, Value Health, 23 (2020), 768–774. https://doi.org/10.1016/j.jval.2020.02.003 doi: 10.1016/j.jval.2020.02.003
[19]	I. Wilson, Clinical understanding and clinical implications of response shift, Soc. Sci. Med., 48 (1999), 1577–1558. https://doi.org/10.1016/S0277-9536(99)00050-7 doi: 10.1016/S0277-9536(99)00050-7
[20]	S. Jansen, A. Sttgelbout, M. Nooij, E. Noordijk, J. Kievit, Response shift in quality of life measurement in early-stage breast cancer patients undergoing radiotherapy, Quality Life Res., 9 (2000), 603–615. https://doi.org/10.1023/A:1008928617014 doi: 10.1023/A:1008928617014
[21]	R. Golembiewski, K. Billingsley, S. Yeager, Measuring change and persistence in human affairs: Types of change generated by OD designs, J. Appl. Behav. Sci., 12 (1976), 133–157. https://doi.org/10.1177/002188637601200201 doi: 10.1177/002188637601200201
[22]	G. S. Howard, P. R. Dailey, Response-shift bias: A source of contamination of self-report measures, J. Appl. Psychol., 64 (1979), 144–150. https://doi.org/10.1037/0021-9010.64.2.144 doi: 10.1037/0021-9010.64.2.144
[23]	P. Norman, S. Parker, The interpretation of change in verbal reports: Implications for health psychology, Psychol. Health, 11 (1996), 301–314. https://doi.org/10.1080/08870449608400259 doi: 10.1080/08870449608400259
[24]	I. Wilson, P. Cleary, Linking clinical variables with related quality of life: A conceptual model of patients outcomes, J. Am. Med. Assoc., 273 (1995), 50–65. https://doi.org/10.1001/jama.273.1.59 doi: 10.1001/jama.273.1.59
[25]	C. C. Rodríguez-Martínez, Contribuciones a los Métodos STATIS Basados en Técnicas de Aprendizaje no Supervisado, Universidad de Salamanca. Ph.D. Thesis, Universidad de Salamanca, Salamanca, Spain, 2020.
[26]	N. B. Erichson, P. Zheng, K. Manohar, S. L. Brunton, J. N. Kutz, A. Y. Aravkin, Sparse principal component analysis via variable projection, J. Am. Med. Assoc., 80 (2020), 977–1002. https://doi.org/10.1137/18M1211350 doi: 10.1137/18M1211350
[27]	M. Cubilla-Montilla, A. B. Nieto-Librero, P. Galindo-Villardón, C. A. Torres-Cubilla, Sparse HJ biplot: A new methodology via elastic net, Mathematics, 9 (2021), 1298. https://doi.org/10.3390/math9111298 doi: 10.3390/math9111298
[28]	C. C.Rodríguez-Martínez, M. Cubilla-Montilla, SparseSTATISdual: R package for penalized STATIS-dual analysis, github.com/CCRM07/SparseSTATISdual (accessed on 15 June 2021)
[29]	S. Ambapour, Statis: Une méthode d'analyse conjointe de plusieurs tableaux de données, Document de travail (DT 01/2001).Bureau d'Application des Methodes Statistiques et Informatiques, pp. 1–20. www.yumpu.com/fr/document/read/37543574 (accessed on 15 June 2021).
[30]	J. C.Laria, M. C. Aguilera-Morillo, E. Álvarez, R. E. Lillo, S. López-Taruella, M. del Monte-Millán, et al., Iterative variable selection for high-dimensional data: Prediction of pathological response in triple-negative breast cancer, Mathematics, 9 (2021), 222. https://doi.org/10.3390/math9030222 doi: 10.3390/math9030222
[31]	E. Ortega-Gómez, P. Vicente-Galindo, H. Martín-Rodero, P. Galindo-Villardon, Detection of response shift in health-related quality of life studies: A systematic review, Health Qual. Life Outcomes, 20 (2022), 20. https://doi.org/10.1186/s12955-022-01926-w doi: 10.1186/s12955-022-01926-w
[32]	T. T.Sajobi, R. Brahmbatt, L. M. Lix, B. D. Zumbo, R. Sawatzky, Scoping review of response shift methods: Current reporting practices and recommendations, Qual. Life Res., 27 (2018), 1133–1146. https://doi.org/10.1007/s11136-017-1751-x doi: 10.1007/s11136-017-1751-x
[33]	H. L'Hermier des Plantes, Structuration des tableaux à trois indices de la statistique, théorie et application d'une méthode d'analyse conjointe, Master's thesis, Université Des Sciences et Techniques Du Languedoc, Montpellier, France, 1976.
[34]	C. Lavit, M. C. Bernard, C. P. Hugalde, M. O. Pernin, Analyse conjointe de tableaux quantitifs, Masson, Paris, France, 1988.
[35]	C. Lavit, Y. Escoufier, R. Sabatier, P. Traissac, The act (STATIS method), Comput. Stat. Data Anal., 18 (1994), 97–119. https://doi.org/10.1016/0167-9473(94)90134-1 doi: 10.1016/0167-9473(94)90134-1
[36]	Y. Escoufier, Opérateur associé à un tableau de données, Annales de Institut National de la Statistique et Des études Économiques, pp. 165–179. https://doi.org/10.2307/20075217
[37]	C. Martin-Barreiro, J. A. Ramirez-Figueroa, X. Cabezas, V. Leiva, M. P. Galindo-Villardón, Disjoint and functional principal component analysis for infected cases and deaths due to COVID-19 in South American countries with sensor-related data. Sensors, 21 (2021), 4094. https://doi.org/10.3390/s21124094 doi: 10.3390/s21124094
[38]	P. Sharma, A. K. Singh, V. Leiva, C. Martin-Barreiro, X. Cabezas, Modern multivariate statistical methods for evaluating the impact of WhatsApp on academic performance: Methodology and case study in India. Appl. Sci., 12 (2020), 6141. https://doi.org/10.3390/app12126141 doi: 10.3390/app12126141
[39]	C. Martin-Barreiro, J. A. Ramirez-Figueroa, A. B. Nieto-Librero, V. Leiva, A. Martin-Casado, M. P. Galindo-Villardón, A new algorithm for computing disjoint orthogonal components in the three-way Tucker model, Mathematics, 9 (2021), 203. https://doi.org/10.3390/math9030203 doi: 10.3390/math9030203
[40]	C. Martin-Barreiro, J. A. Ramirez-Figueroa, X. Cabezas, V. Leiva, A. Martin-Casado, M.P. Galindo-Villardón, A new algorithm for computing disjoint orthogonal components in the parallel factor analysis model with simulations and applications to real-world data, Mathematics, 9 (2021), 2058. https://doi.org/10.3390/math9172058 doi: 10.3390/math9172058
[41]	H. Abdi, D. Valentin, D. In, D. Z. Valentin, L. Nguyen, New trends in sensory evaluation of food and non-food products, Vietnam National University, Ho Chi Minh City Publishing House, 2007, pp. 5–18.
[42]	K. Tarczy-Hornoch, M. Ying-Lai, R. Varma, Los Angeles Latino Eye Study Group, Myopic refractive error in adult Latinos: The Los Angeles Latino eye study. Invest. Ophthalmol. Visual Sci., 47 (2006), 1845–1852. https://doi.org/10.1167/iovs.05-1153 doi: 10.1167/iovs.05-1153
[43]	S. Kay, A. Ferreira, Mapping the 25-item national eye institute visual functioning questionnaire (NEI VFQ-25) to EQ-5D utility scores, Ophth. Epidemiol., 21 (2014), 66–78. https://doi.org/10.1007/s12325-016-0333-6 doi: 10.1007/s12325-016-0333-6
[44]	J. R.Grubbs, S. Tolleson-Rinehart, K. Huynh, R. M. Davis, A review of quality of life measures in dry eye questionnaires, Cornea, 33 (2014), 215–218. https://doi.org/10.1007/s12325-016-0333-6 doi: 10.1007/s12325-016-0333-6
[45]	L. Quaranta, I. Riva, C. Gerardi, F. Oddone, I. Floriano, A. G. Konstas, Quality of life in glaucoma: A review of the literature, Adv. Therapy, 33 (2016), 959–981. https://doi.org/10.1007/s12325-016-0333-6 doi: 10.1007/s12325-016-0333-6
[46]	F. Kuhn, R. Morris, C. D. Witherspoon, K. Heimann, J. B. Jeffers, G. Treister, A standardized classification of ocular trauma, Ophthalmology, 103 (1996), 240–243. https://doi.org/10.1016/S0161-6420(96)30710-0 doi: 10.1016/S0161-6420(96)30710-0
[47]	R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, 2021.
[48]	C. C. Rodríguez-Martínez, M. Cubilla-Montilla, P. Vicente-Galindo, P. Galindo-Villardón, Sparse STATIS-dual via elastic net, Mathematics, 9 (2021), 2094. https://doi.org/10.1016/j.msard.2016.11.008 doi: 10.1016/j.msard.2016.11.008
[49]	F. Schmidt, H. Zimmermann, J. Mikolajczak, F. C. Oertela, F. Pache, M. Weinhold, et al., Severe structural and functional visual system damage leads to profound loss of vision-related quality of life in patients with neuromyelitis optica spectrum disorders, Multi. Scler. Related Disord., 11 (2017), 45–50. https://doi.org/10.1016/j.msard.2016.11.008 doi: 10.1016/j.msard.2016.11.008
[50]	L. Bradnam, C. Chen, L. Graetz, T. Loetscher, Reduced vision-related quality of life in people living with dystonia, Disab. Rehabil., 42 (2020), 1556–1560. https://doi.org/10.1080/09638288.2018.1528636 doi: 10.1080/09638288.2018.1528636
[51]	D. Yuan, W. Zhang, S. Yuan, P. Xie, Q. Liu, Evaluation of vision-related quality of life after autologous internal limiting–membrane transplantation for refractory macular holes, Clin. Ophthalmol., 14 (2020), 2079–2085. https://doi.org/10.2147/OPTH.S259642 doi: 10.2147/OPTH.S259642
[52]	M. Li, L. Gong, W.J. Chapin, M. Zhu, Assessment of vision-related quality of life in dry eye patients, Invest. Ophthalmol. Visual Sci., 53 (2012), 5722–5727. https://doi.org/10.1167/iovs.11-9094 doi: 10.1167/iovs.11-9094
[53]	G. Ilie, J. Bradfield, L. Moodie, T. Lawen, A. Ilie, Z. Lawen, et al., The role of response-shift in studies assessing quality of life outcomes among cancer patients: A systematic review. Front. Oncol., 9 (2019), 783. https://doi.org/10.3389/fonc.2019.00783 doi: 10.3389/fonc.2019.00783
[54]	A. Ousmen, T. Conroy, F. Guillemin, M. Velten, D. Jolly, M. Mercier, et al., Impact of the occurrence of a response shift on the determination of the minimal important difference in a health-related quality of life score over time, Health Qual. Life Outcomes, 14 (2016), 167. https://doi.org/10.1186/s12955-016-0569-5 doi: 10.1186/s12955-016-0569-5
[55]	J. A.Haagsma, I. Spronk, M. A. de Jongh, G. J. Bonsel, S. Polinder, Conventional and retrospective change in health-related quality of life of trauma patients: An explorative observational follow-up study, Health Qual. Life Outcomes, 18 (2020), 157. https://doi.org/10.1186/s12955-020-01404-1 doi: 10.1186/s12955-020-01404-1
[56]	B. Hosseini, S. Nedjat, K. Zendehdel, R. Majdzadeh, A. Nourmohammadi, A. Montazeri, Response shift in quality of life assessment among cancer patients: A study from Iran, Med. J. Islamic Republic Iran, 31 (2017), 120. https://doi.org/10.2106/JBJS.I.00990 doi: 10.2106/JBJS.I.00990
[57]	H. Razmjou, C. E. Schwartz, R. Holtby, The impact of response shift on perceived disability two years following rotator cuff surgery, J. Bone Joint Surgery, 92 (2010), 2178–2186. https://doi.org/10.2106/JBJS.I.00990 doi: 10.2106/JBJS.I.00990
[58]	X. H. Zhang, S. C. Li, F. Xie, N. N. Lo, K. Y. Yang, S. J. Yeo, et al., An exploratory study of response shift in health-related quality of life and utility assessment among patients with osteoarthritis undergoing total knee replacement surgery in a tertiary hospital in Singapore, Value Health, 15 (2012), S72–S78. https://doi.org/10.1016/j.jval.2011.11.011 doi: 10.1016/j.jval.2011.11.011
[59]	M. Rutgers, L. B. Creemers, K. G. A. Yang, N. J. Raijmakers, W. J. Dhert, D. B. Saris, Osteoarthritis treatment using autologous conditioned serum after placebo: Patient considerations and clinical response in a non-randomized case series, Acta Orthopaed., 86 (2015), 114–118. https://doi.org/10.3109/17453674.2014.950467 doi: 10.3109/17453674.2014.950467
[60]	C. Machuca, M. V. Vettore, P. G. Robinson, How peoples' ratings of dental implant treatment change over time? Qual. Life Res., 29 (2020), 1323–1334. https://doi.org/10.1007/s11136-019-02408-1 doi: 10.1007/s11136-019-02408-1
[61]	H. Y. Shi, K. T. Lee, H. H. Lee, Y. H. Uen, C. C. Chiu, Response shift effect on gastrointestinal quality of life index after laparoscopic cholecystectomy, Qual. Life Res., 20 (2011), 335–341. https://doi.org/10.1007/s11136-010-9760-z doi: 10.1007/s11136-010-9760-z
[62]	Y. Edelaar-Peeters, A. M. Stiggelbout, Anticipated adaptation or scale recalibration?, Health Qual. Life Outcomes, 11 (2013), 171. https://doi.org/10.1186/1477-7525-11-171 doi: 10.1186/1477-7525-11-171
[63]	M. Ramos-Barberán, M. V. Hinojosa-Ramos, J. Ascencio-Moreno, F. Vera, O. Ruiz-Barzola, M. P. Galindo-Villardón, Batch process control and monitoring: A dual STATIS and parallel coordinates (DS-PC) approach, Product. Manuf. Res., 6 (2018), 470–493. https://doi.org/10.1080/21693277.2018.1547228 doi: 10.1080/21693277.2018.1547228
[64]	J. L. da Silva, L. P. Ramos, Uniform approximations for distributions of continuous random variables with application in dual STATIS method, REVSTAT Stat. J., 12 (2014), 101–118.
[65]	R. Boumaza, S. Yousfi, S. Demotes-Mainard, Interpreting the principal component analysis of multivariate density functions. Commun. Stat. Theory Methods, 44 (2015), 3321–3339. https://doi.org/10.1080/03610926.2013.824103 doi: 10.1080/03610926.2013.824103
[66]	S. Klie, C. Caldana, Z. Nikoloski, Compromise of multiple time-resolved transcriptomics experiments identifies tightly regulated functions, Front. Plant Sci., 3 (2012), 249. https://doi.org/10.3389/fpls.2012.00249 doi: 10.3389/fpls.2012.00249
[67]	K. Haraldstad, A. Wahl, R. Andenæs, J. R. Andersen, M. H. Andersen, E. Beisland, et al., A systematic review of quality of life research in medicine and health sciences, Qual. Life Res., 28 (2019), 2641–2650. https://doi.org/10.1007/s11136-019-02214-9 doi: 10.1007/s11136-019-02214-9
[68]	H. L'Hermier des Plantes, Structuration des tableaux à trois indices de la statistique. Université de Montpellier Ⅱ, Montpellier, France, 1976.
[69]	P. A.Jaffrenou, Sur L'Analyse des familles finies des variables vectorielles: Bases algébrique et application à la description statistique, University of Sainte-Etiene, Sainte-Etiene, France, 1978.
[70]	Y. Escoufier, L'analyse conjointe de plusieurs matrices de données, In Jolivet, M. (ed.), Biométrie et Temps. Société Française de Biométrie, Paris, France, pp. 59–76.
[71]	J. Martín-Rodríguez, M. P. Galindo-Villardón, J. L. Vicente-Villardón, Comparison and integration of subspaces from a biplot perspective, J. Stat. Plan Infer., 102 (2002), 411–423. https://doi.org/10.1016/S0378-3758(01)00101-X doi: 10.1016/S0378-3758(01)00101-X
[72]	A. Vallejo-Arboleda, J. L. Vicente-Villardón, M. P. Galindo-Villardón, Canonical STATIS: Biplot analysis of multi-table group structured data based on STATIS-ACT methodology, Comput. Stat. Data Anal., 51 (2007), 4193–4205. https://doi.org/10.1016/j.csda.2006.04.032 doi: 10.1016/j.csda.2006.04.032
[73]	J. Bénasséni, M. Bennani-Dosse, Analyzing multiset data by the power STATIS-ACT method, Adv. Data Anal. Classif., 6 (2012), 49–65. https://doi.org/10.1007/s11634-011-0085-8 doi: 10.1007/s11634-011-0085-8
[74]	H. Abdi, L. J. Williams, D. Valentin, M. Bennani-Dosse, STATIS and DISTATIS: Optimum multitable principal component analysis and three way metric multidimensional scaling, Comput. Stat., 4 (2012), 124–167. https://doi.org/10.1002/wics.198 doi: 10.1002/wics.198
[75]	F. Llobell, V. Cariou, E. Vigneau, A. Labenne, E. M. Qannari, A new approach for the analysis of data and the clustering of subjects in a CATA experiment, Food Qual. Prefer., 72 (2019), 31–39. https://doi.org/10.1016/j.foodqual.2018.09.006 doi: 10.1016/j.foodqual.2018.09.006
[76]	F. Llobell, V. Cariou, E. Vigneau, A. Labenne, E. M.Qannari, Analysis and clustering of multiblock datasets by means of the STATIS and CLUSTATIS methods. Application to sensometrics, Food Qual. Prefer., 79 (2020), 103520. https://doi.org/10.1016/j.foodqual.2018.05.013 doi: 10.1016/j.foodqual.2018.05.013
[77]	B. R. Lapin, Considerations for reporting and reviewing studies including health-related quality of life, Chest, 158 (2020), S49–S56. https://doi.org/10.1016/j.chest.2020.03.007 doi: 10.1016/j.chest.2020.03.007
[78]	S. Wang, X. Liang, J. Wang, Parameter assignment for InVEST habitat quality module based on principal component analysis and grey coefficient analysis, Math. Biosci. Eng., 19 (2022), 13928–13948. https://doi.org/10.3934/mbe.2022649 doi: 10.3934/mbe.2022649
[79]	M. R. M. Visser, E. M. A. Smets, M. A. G. Sprangers, H. J. C. J. M. De Haes, How response shift may affect the measurement of change in fatigue, J. Pain Sympt. Manag., 20 (2000), 12–18. https://doi.org/10.1016/S0885-3924(00)00148-2 doi: 10.1016/S0885-3924(00)00148-2
[80]	L. G.Hill, D. L. Betz, Revisiting the retrospective pretest, Am. J. Evalu., 26 (2005), 501–517. https://doi.org/10.1177/1098214005281356 doi: 10.1177/1098214005281356
[81]	J. A. Ramirez-Figueroa, C. Martin-Barreiro, A. B. Nieto-Librero, V. Leiva, M. P. Galindo-Villardón, A new principal component analysis by particle swarm optimization with an environmental application for data science, Stoch. Environ. Res. Risk Assess., 35 (2021), 1969–1984. https://doi.org/10.1007/s00477-020-01961-3 doi: 10.1007/s00477-020-01961-3

This article has been cited by:

1.	Chengxi Wu, Yuewei Dai, Liang Shan, Zhiyu Zhu, Date-Driven Tracking Control via Fuzzy-State Observer for AUV under Uncertain Disturbance and Time-Delay, 2023, 11, 2077-1312, 207, 10.3390/jmse11010207
2.	Zhenzhong Chu, Zhenhao Gu, Zhiqiang Li, Yunsai Chen, Mingjun Zhang, A fault diagnostic approach based on PSO-HMM for underwater thrusters, 2022, 19, 1551-0018, 12617, 10.3934/mbe.2022589
3.	Liwei Guo, Weidong Liu, Le Li, Jingming Xu, Kang Zhang, Yuang Zhang, Fast Finite-Time Super-Twisting Sliding Mode Control with an Extended State Higher-Order Sliding Mode Observer for UUV Trajectory Tracking, 2024, 8, 2504-446X, 41, 10.3390/drones8020041
4.	Tomasz Praczyk, Maciej Szymkowiak, Linear matrix genetic programming as a tool for data-driven black-box control-oriented modeling in conditions of limited access to training data, 2024, 14, 2045-2322, 10.1038/s41598-024-63419-8
5.	Rui Xu, Hua Chen, Yao Tang, Xinyuan Long, Model-free predictive iterative learning safety-critical consensus control for multi-agent systems with randomly varying trial lengths, 2025, 196, 01676911, 105987, 10.1016/j.sysconle.2024.105987
6.	Liyu Lu, Haoliang Wang, Nan Gu, Zhouhua Peng, Weidong Zhang, Distributed Cooperative Guidance Model-Free Control for a Cluster of Disk-Type Autonomous Underwater Gliders, 2025, 22, 1545-5955, 12395, 10.1109/TASE.2025.3543530

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Mathematical Biosciences and Engineering

4.4

Metrics

Article views(2272) PDF downloads(122) Cited by(1)

Preview PDF

Download XML

Export Citation

Article outline

Show full outline

Figures and Tables

Figures(6) / Tables(4)

Mathematical Biosciences and Engineering

STATIS multivariate three-way method for evaluating quality of life after corneal surgery: Methodology and case study in Costa Rica

Related Papers:

Abstract

1. Introduction

2. Intellectual capital and high-techs firms' financing choices

3. Data, variables and method

3.1. Database

3.2. Estimation method and variable measurement

3.2.1. Static panel data model

3.2.2. Dynamic panel data model

4. Empirical results

4.1. Descriptive statistics and correlation matrix

4.2. GMM system results

5. Discussion of the results

6. Conclusion

Acknowledgments

Conflict of interest

References

This article has been cited by:

Reader Comments

通讯作者: 陈斌, bchen63@163.com

Metrics

Figures and Tables

Other Articles By Authors

Catalog

Mathematical Biosciences and Engineering

STATIS multivariate three-way method for evaluating quality of life after corneal surgery: Methodology and case study in Costa Rica

Related Papers:

Abstract

1. Introduction

2. Intellectual capital and high-techs firms' financing choices

3. Data, variables and method

3.1. Database

3.2. Estimation method and variable measurement

3.2.1. Static panel data model

3.2.2. Dynamic panel data model

4. Empirical results

4.1. Descriptive statistics and correlation matrix

4.2. GMM system results

5. Discussion of the results

6. Conclusion

Acknowledgments

Conflict of interest

References

This article has been cited by:

Reader Comments

通讯作者: 陈斌, bchen63@163.com

Metrics

Figures and Tables

Other Articles By Authors

Related pages

Tools

Export File

Citation

Format

Content

Catalog