Correlation Analysis

Correlation analyses using the Pearson correlation coefficient have been carried out in order to understand the relationship between the leader and the follower. The study clearly reinforces the relation between the leader’s group atmosphere and the support from members and also the group cohesiveness of the members. The respondents were given nine parameters under each head- group atmosphere and support from members (leaders) and group cohesiveness (members).Their response is given as scores 1- Highly Dissatisfied, 2- Dissatisfied, 3-Moderate, 4- Satisfied, 5- Highly Satisfied.

Apart from the above indicated tools of analysis several other econometric analysis have also been done for the validation of the appropriate results.Most of the analysis has been done in the most relevant software of the present times such as R, SAS, and SPSS. All the major econometric analysis used in different chapters are indicated below.

(i) PCA and Factor analysis

Principal Component Analysis and Factor analysis were used as the major analysis in the present study.The positive changes of the activity groups,rating of the activity groups on the basis of the performance on technical/institutional/economic and social,benefits gained by the leader as well as the follower, short comings in the current functioning, group atmosphere and support from members,reasons for drop out etc. were first analysed using PCA in order to assess the variation and further subjected to the factor analysis for detecting the amount of variation by each factor and there by major factors for the respective parameters are found out.

The concept of PCA and factor analysis is as follows.

PCA is a dimension-reduction tool that can be used to reduce a large set of variables to a small set that still contains most of the information in the large set. The goal is dimension reduction and there is no guarantee that the dimensions are interpretable. With PCA, unities are used in the diagonal of the correlation matrix computationally implying that all the variance is common

or shared. PCA seeks a linear combination of variables such that the maximum variance is extracted from the variables. It then removes this variance and seeks a second linear combination which explains the maximum proportion of the remaining variance, and so on.

Factor analysis investigates the variable relationships for complex concepts of positive changes, rating of the groups on performance etc. It allows investigating concepts that are not easily measured directly by collapsing a large number of variables into a few interpretable underlying factors.The key concept of factor analysis is that multiple observed variables have similar patterns of responses because they are all associated with a latent (i.e. not directly

Deciding how many factors are useful to retain will be the subject of another post.

(ii) Structural equation Modelling

In order to identify the major driving forces of women empowerment structural equation modelling was used. Since majority of the data included are of ordinal type we cannot measure the estimated value of the empowerment level of the women involved in the activity groups.

Structural equation modelling is used in order for finding the relationship of the various parameters and the empowerment level. Satorra-Bentler scaled Chi-Square and Root Mean Square Error Approximation (RMSEA) is used to estimate the accurate value of the present empowerment and the major driven parameters that lead such empowerment.

The respondents were choose to give scores for the parameters indicated for each empowerment indicator as 1-Very High, 2-High, 3-Average, 4-Low, 5-Very Low.Moreover, considering the different categories of the responses to this question, it is difficult to know by how much more the respondent reacts if she would have chosen category 4 over category 5.

Secondly, even if the respondent chooses category 4, for instance, we don’t know the magnitude of her empowerment strategy. Furthermore, even if two different respondents choose the same category 4, we cannot say that their magnitude of their empowerment level in the corresponding section is the same.

The synchronized equations of structural equation (i) connected through the relevant signs. The dimension model matches to the left part of the path diagram

The latent women’s empowerment is represented by and is computed by the indicator vector y as presented by means of equation (ii), where is the vector of factor loadings and is the vector of quantity errors related through y. The dimension model matches to the right-hand part of path diagram

Equation (iii) is the SEM model, that specifies the latent women empowerment depends on the vector of latent component , where is the vector of latent regression coefficients and is the error word. The statistical significance of the latent regression coefficients thus point out which latent component has a noteworthy impact empowerment of women.

(iii) Stepwise Regression

The stepwise regression analysis was used to find the major driven factor for the group to be an innovator and laggard.It underlies the existing relationship between the assets created and the expenditure, profits shared, income etc.

The step-by-step iterative construction of a regression model involves automatic selection of independent variables. Stepwise regression can be achieved either by trying out one independent variable at a time and including it in the regression model if it is not under significant, or by including all potential independent variables in the model and eliminating those that are not statistically significant, or by a combination of both methods. It includes the following procedures.

 Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model comparison criterion, adding the variable (if any) that improves the model the most, and repeating this process until none improves the model.

 Backward elimination, which involves starting with all candidate variables, testing the deletion of each variable using a chosen model comparison criterion, deleting the variable (if any) that improves the model the most by being deleted, and repeating this process until no further improvement is possible.

 Bidirectional elimination, a combination of the above, testing at each step for variables to be included or excluded.

This is an automatic procedure for statistical model selection in cases where there is a large number of potential explanatory variables, and no underlying theory on which to base the model selection. The procedure is used primarily in regression analysis, though the basic approach is applicable in many forms of model selection. This is a variation on forward selection and at each stage in the process, after a new variable is added; a test is made to check if some variables can be deleted without appreciably increasing the residual sum of squares (RSS). The procedure terminates when the measure is (locally) maximized, or when the available improvement falls below some critical value.

Section - IV