The choice of the right statistical methods depends on the nature of the data collected and the relationship between the methods and the research objectives. As a result, this study used what is relevant to the research questions and framework in tandem with the data collected. The data analysis techniques were two-fold. Firstly, the secondary data analysis used a panel regression technique and in the second stage, the survey, that is, the primary data obtained through administered questionnaires (Appendix 1), used a logistic regression technique. The triangulation of the two results may eventually reveal the strengths inherent in these models and reduce any weaknesses therein. Chapters Six and Eight presents the analyses of the models using the two techniques, that is, the panel regression and the logistic regression techniques. The subsequent subsections highlight what to expect in the next chapter.
5.9.1 Quantitative data analysis of secondary data
The study employed panel regression to analyse the secondary quantitative data. It used Pool, Static and Feasible generalised least square (FGLS) groupwise panel data models to examine the effect of audit committee attributes on RAM of listed firms on NSE. In testing and analysing the various formulated hypotheses, the study used the STATA statistical package as an analytical tool. The analysis comprised the following:
133 5.9.1.1 Pool model
The pooled model could be a usual starting point to group the data together and average out the individual-effects. Pool model assumes a similar slope and a similar intercept over all cross-sections. The model restrictively means that all coefficients (slopes and intercepts) are similar over time and cross-sections. The unrestricted model allows slope and intercepts coefficients to vary over time and cross-sections (Cameron & Trivedi, 2010).
5.9.1.2 Breusch Pagan Lagrange Multiplier (LM) test for random effects
The Breusch-Pagan LM test will test the most appropriate model between the pool and the random-effects model. The test is used to support the decision of using the random- effect model. This test comes immediately after estimating a random-effect model. It helps to determine the most appropriate model to rely on between the estimates of the random effect panel model and the pooled model.
5.9.1.3 Static panel analysis
Static panel data comprises mainly of fixed and random effects models. In the fixed effects approach, unobserved effects are the fixed parameters to be estimated and correlate with the exogenous variables. The observations of the exogenous variables are independent of the idiosyncratic error term for all cross-sections or periods. Baltagi (2005) notes that it is a proper specification if the focus is on a specific set of companies and inference is limited to the same set of companies. It is an appropriate specification for most accounting research (de Jager, 2008).
In a random-effects approach, the unobserved effects parameters are presumed to be random and are independent of the idiosyncratic error term. In addition, the total error and the observations of the exogenous variables are independent for all cross-sections or periods. The random-effects approach is suitable when making random draws from a large population (when the sample size is approaching infinity) to develop inferences about the population features.
However, an essential criterion for using static panel data is that all the variables to be included in the panel model must be stationary (Blundell & Bond, 1998). Therefore, to check for stationarity, the study conducted a panel unit root test and presents the results in Chapter Six. The analysis implies that all the variables are suitable for panel model estimation, and it minimises the tendency of yielding spurious regression results.
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It is appropriate to choose between the different panel models. Firstly, it is usual to test for the presence of unobserved/individual-specific effects in the model. Fixed effects will use the Fischer (F) test while random effects will use the Breusch and Pagan's Lagrange Multiplier (LM) test (Park, 1967). Following Park (1967), the F-test resolves whether fixed effects or the pooled ordinary least squares better fits the panel data, whereas the LM-test determines between the random effects and pooled ordinary least squares.
a) The fixed effects (F-test) is a test for the null hypothesis that all individual intercepts are equal to zero in the regression model. More specifically, the result is an F-statistic, that quantifies by how much the goodness-of-fit has changed (Park, 1967).
b) The random effects (Breusch-Pagan LM test) is a test for the null hypothesis that all individual-specific variance components are zero, in the regression model.
5.9.1.4 Choosing between fixed effects and random effects (Hausman test)
The peculiarity between the covariance and error component in panel data analysis is crucial. It becomes appropriate to test for the existence of a correlation between the specific error term and the regressors. The Hausman test assesses the appropriateness of the random effect’s estimator. Indeed, it tests for the null hypothesis that individual- specific effects are random. More specifically, a Hausman test checks if there are no systematic differences between the coefficient estimators of the two models (Baum, 2001). Under the null hypothesis, both estimators are consistent, and the estimators should display similar results, whereas under the alternative hypothesis, one estimator widely differs from the consistent estimator (Cameron & Trivedi, 2010). Considering this, the random effects estimator is consistent and more efficient than the fixed effects estimator under H0 while only fixed effects remain consistent under the alternative.
The Hausman test compares the estimates from the two models to determine which is more consistent. If the probability (p)-value is significant (for example, <0.05) then use fixed effects, if not use random effects (Greene, 2008; Reyna, 2010). As stated earlier, it tests whether the unique errors (ui) correlates with the regressors, and the null hypothesis states that they are not.
135 5.9.2 Diagnostic tests
5.9.2.1 Model errors structure
The idiosyncratic errors assume to generate in a spherical manner and thus satisfied the classical ordinary least square assumptions about homoscedasticity and correlation.
However, panel data structures often violate these standard assumptions about the error process (Podestà, 2002). So, it becomes imperative to check for these standard assumptions. The assumptions concerning homoskedasticity, cross-sectional correlation (contemporaneous correlation) and autocorrelation within units (serial correlation).
These checks are of primary importance to avoid the findings being statistically spurious. Next is the diagnostic of the residuals of the individual fixed-effects model.
5.9.2.2 Testing for heteroskedasticity
In many panel datasets, the variance among cross-sectional units can differ. Among the reasons responsible for this phenomenon, it is possible to quote differences in the scale of the dependent variable between units. In consequence, it is appropriate to perform a modified Wald test to detect the existence of group-wise heteroskedasticity in the residuals of fixed-effect regression. Under the null hypothesis, the variance of the error is the same for all individual effect (Baum, 2001).
5.9.2.3 Testing for cross-sectional correlation
The impact of cross-sectional dependence on dynamic panel estimators is severe.
Phillips and Sul (2003) show that ignoring cross-sectional dependence in the data during estimation is inappropriate. The decrease in estimation efficiency can become so large that, in fact, the pooled (panel) least-squares estimator may provide little gain over the single-equation ordinary least squares. This check is crucial to avoid the consequences that may occur to the result of the estimation. It implies pooling a population of cross-sectional data that are homogeneous but ignores cross-sectional dependence. The gains on efficiency in comparison with running individual ordinary least squares regressions for each cross-section may largely reduce.
It is essential also to note that a deviation from idiosyncratic errors could result from the contemporaneous correlation of errors across units. It is necessary to test for cross- sectional dependence in the error term using the Pesaran’s test of cross-sectional independence.
136 5.9.2.4 Testing for autocorrelation within units
Serial correlation in linear panel-data models biases the standard errors and causes the results to be less efficient. It becomes imperative to identify serial correlation in the idiosyncratic error term in a panel-data model. There are numerous tests for serial correlation in panel-data models in the literature, and the analysis put forward by Wooldridge (2013) is attractive because it requires relatively few assumptions and is easy to implement.
According to Tsionas (2019), serial correlation is responsible for too optimistic standard errors. It is appropriate to check for this complication by performing a Wooldridge test where the null hypothesis assumes no first-order autocorrelation.