Multiple Regression Analysis

Regression analysis is a statistical procedure for estimating the relationships among predictor and predicted variables. The primary purpose of this technique is focused on the

Sl. No. Author Year Dimensions

1 Chaston, et al. 2001

The study has been undertaken to acquire data on whether a relationship exists between learning style and the competencies exhibited by organisations.

2 Murray 2003

An empirical investigation, determining the relationship between the creation of competencies and the quality of learning within an organisation.

3 Thach and Thompson 2007

Identifies differences that exist in leadership style, behaviours, and competencies to drive performance between profit and non‐profit organisational leaders.

4 Sudsakorn and

Swierczek 2009

Investigates the management competencies required by global business manager in a business environment.

5 Milicevic, et al. 2011

This study explores the competencies and the perceived competence gap of management personnel in public primary health care.

6 Yang, et al. 2012

Investigates the relationship of the project leader’s competencies with job satisfaction, and their impact on project performance

7 L. Zhang and W. Fan 2013

This study makes recommendations on the selection and appointment of project managers in construction organisations by recognising the significant emotional competencies that can cater for large and complex construction projects.

8 Verle, et al. 2014

Determines whether there is a relationship among leadership, action, social, and personal competencies of managers in modern organisational structure types and whether a relationship exists between a company’s organisational structure and performance.

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relationship between a dependent variable and one or more independent variables. It is a way of predicting an outcome variable from one independent variable or several independent variables (Field, 2009). When one independent variable is involved, it is known as simple regression, whereas in the case of more than one independent variable it is known as multiple regressions. Multiple regressions are a statistical technique used to analyse the relationship between a single dependent variable and several independent variables, wherein each independent variable is weighted by the regression analysis procedure to ensure maximal prediction from the set of independent variable (Hair, et al., 2009).

According to Hair, et al. (2009) multiple regressions fulfil two objectives of the research. Firstly, to maximise the overall predictive power of the independent variables as represented in the variate and secondly, to compare two or more sets of independent variables to ascertain the predictive power of each variate. The size of the sample has a direct impact on the appropriateness and the statistical power of the multiple regression analysis, therefore the researcher must ensure that the criterion of practical significance is met along with statistical significance. As a rule of thumb the minimum ratio of observations to variable is 5:1, but the preferred ratio is 15:1 or 20:1, which increases with stepwise estimation. Likewise, maximising the degree of freedom improves the generalisability of the model parsimony and the concerns regarding the sample size. The table 6.4 illustrates some relevant studies which have used multiple regression analysis for the purpose of data interpretation.

Table 6.4: Relevant Studies Undertaking Multiple Regression Analysis

Sl. No. Author Year Dimensions

1 McCredie and

Shackleton 2000

Explores the requisite competencies of subsidiary unit general managers in a successful multi-business group dealing primarily in industrial goods.

2 Agut, et al. 2003

Analyses the influence of individual and contextual factors (type of establishment and number of subordinates) on managerial competency needs.

3 Hopkins and

Bilimoria 2008

The study highlights the moderating influence of gender between the demonstration of emotional and social intelligence competencies and success.

4 Azan and

Bollecker 2011

Analyses the developments in IT and their significant impact on competencies within an organisational set- up.

5 Ryan, et al. 2012 This study empirically links competencies of individual leaders to business profitability and

~ 165 ~ 6.2.5 Confirmatory Factor Analysis

The confirmatory factor analysis (CFA) is a statistical technique used to verify the factor structure of a set of observed variables, as well as it allows testing of the hypothesis so as to verify the relationship between observed variables and their existing underlying latent constructs. This technique is based on the framework of structural equation modelling procedure. In simple words, CFA is a tool that enables a researcher to confirm or reject one’s preconceived theory. It is used to formulate a confirmatory test of a measurement theory. The measurement theory specifies a series of relationships that suggest how measured variables represent a latent construct that is not measured directly. Through the implementation of CFA, a researcher specifies five elements; the latent constructs, the measured variables, the item loadings on specific constructs, the relationship between constructs and the error terms for each indicator (Hair, et al., 2009). According to Schumacker and Lomax (1996), the use of the CFA can be impacted by various attributes such as; the research hypothesis being tested, the requirement of sufficient sample size, measurement instrument, multivariate normality, parameter identification, outliers, missing data and interpretation of model fit indices.

Most of the statistical methods require only one statistical test to determine the significance of an analysis. However, in CFA, several statistical tests are used to determine, how well the model fits to the data (Suhr, 2006). While reporting the results of a confirmatory factor analysis, one is urged to report; the proposed models, any modifications made, measures identified for each latent variable, correlations between latent variables, any other pertinent information and whether the constraints are used. According to Kline (2010), chi-squared test, the root mean square error of approximation (RMSEA), the comparative fit index (CFI), the goodness of fit index (GFI), the adjusted goodness of fit index (AGFI) and

demonstrate that competencies are cross‐culturally valid.

6 Stavrou and

Ierodiakonou 2013

Utilisation of competency-based models to explore empirically the factors that influence the suitability of different flexible work arrangements in organisations. 7 Fleisher, et al. 2014

Examines the effects of employee’s career competencies on the employing organisation and assessment of career satisfaction in this relationship.

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the standardised root mean square residual (SRMR) must be reported. The chi-squared test indicates the difference between observed and expected covariance matrices and the values closer to zero indicates a better fit as well as smaller variance between expected and observed covariance matrices. The chi-squared statistics can also be used to directly compare the fit of nested models to the data. The RMSEA analyses the discrepancy between the hypothesised model, with optimally chosen parameter estimates, and the population covariance matrix. The value of RMSEA ranges from 0 to 1 and the smaller values indicating a better model fit. Preferably, a value of .06 or less is indicative of acceptable model fit in a study. The CFI analyses the model fit by examining the discrepancy between the data and the hypothesised model, while adjusting for the issues of sample size inherent in the chi-squared test of model fit and the normed fit index. The value of CFI values ranges from 0 to 1 and the value of .90 or larger is generally considered to indicate acceptable model fit. The GFI is a measure of fit between the hypothesised model and the observed covariance matrix. The value of GFI ranges between 0 to 1 and generally a value of .90 is indicative of an acceptable model fit. The AGFI corrects the GFI, which is affected by the number of indicators of each latent variable. The value of AGFI ranges between 0 to 1 and generally a value of .90 is indicative of an acceptable model fit. The SRMR are the square root of the discrepancy between the sample covariance matrix and the model covariance matrix. The value of SRMR ranges from 0 to 1 and a value of .08 or less are indicative of an acceptable model (Hooper, Coughlan and Mullen, 2008). If model fit is acceptable, the parameter estimates are examined. The unstandardised parameter estimates retain scaling information of variables and can only be interpreted with reference to the scales of the variables, while standardised parameter estimates are transformations of unstandardised estimates that removes scale and can be used for informal comparisons of parameters throughout the model.