In most of the studies tobit regression is used but in tobit model my independent variable is not significant. Whether fractional logistic regression is also an appropriate technique to explore determinants of efficiency?
When using efficiency scores as a dependent variable in subsequent regression analysis, researchers often encounter the issue of these scores being bounded between 0 and 1, which violates the assumption of unboundedness in standard linear regression models. To address this issue, fractional regression models, such as the fractional logistic regression, are employed as they are designed specifically for dependent variables that are proportions or percentages confined to the (0,1) interval.
Fractional logistic regression, based on the quasi-likelihood estimation, can be used to model relationships where the dependent variable is a fraction or proportion, which is exactly the nature of technical efficiency scores resulting from DEA. Therefore, it is suitable to apply fractional logistic regression in a two-stage DEA analysis where the first stage involves calculating the efficiency scores, and the second stage seeks to regress these scores on other explanatory variables to investigate what might influence the efficiency of the DMUs.
This two-stage approach, where the DEA is used first to compute efficiency scores and then fractional logistic regression is used in the second stage, helps to avoid the potential biases and inconsistencies that might arise if standard linear regression techniques were used with bounded dependent variables. It is an appropriate statistical technique for dealing with the special characteristics of efficiency scores and can provide more reliable insights into the factors influencing DMU efficiency.
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