Darryl Laws

 Log likelihood. Had I conducted the research I would have chosen to use log likelihood statistic to assess and to depict the deviance, or -2 log-likelihood (-2LL) statistic. The deviance is basically a measure of how much unexplained variation there is in our logistic regression model the higher the value the less accurate the model. It compares the difference in probability between the predicted outcome and the actual outcome for each case and sums these differences together to provide a measure of the total error in the model. This is similar in purpose to looking at the total of the residuals (the sum of squares) in linear regression analysis in that it provides us with an indication of how good our model is at predicting the outcome. The -2LL statistic (often called the deviance) is an indicator of how much unexplained information there is after the model has been fitted, with large values of -2LL indicating poorly fitting models. 

The deviance has little intuitive meaning because it depends on the sample size and the number of parameters in the model as well as on the goodness of fit. Therefore, we need a standard to help us evaluate its relative size. One way to interpret the size of the deviance is to compare the value for our model against a baseline model. In linear regression we learned how SPSS performs an ANOVA to test whether or not the model is better at predicting the outcome than simply using the mean of the outcome. The change in the -2LL statistic can be used to do something similar: to test whether the model is significantly more accurate than simply always guessing that the outcome will be the more common of the two categories. We use this as the baseline because in the absence of any explanatory variables the best guess will be the category with the largest number of cases.

Is potential endogeneity addressed? An endogenous variable in statistics is a variable in a statistical model that is changed or determined by relationships with other variables in the model. Often it is synonymous with the dependent variable…meaning that it correlates with other factors within the study. An endogenous regressor is one that is correlated with or has non-zero variance with the random error term in the equation (Investopedia). Malmendier and Tate’s (2008)  article goes to tremendous strains to correlate the independent variable CEO overconfidence’s impact upon the dependent variables; holding their personal stock options until maturity and overly acquisitiveness through investigating the various outcomes and impacts that the predictor variable impose on each; i.e. the press ramifications on the public’s and shareholder’s respective perceptions of over confident CEOs in adjunct to their assessment of the capital market’s impact due to similar perceptions the overconfident CEO.     

Darryl Laws