Darryl Laws

 The measurement they use is the coefficient odds ratio (log likelihood statistic). The odds ratio is crucial to the interpretation of logistics regression. It is an indicator of the change in odds resulting from a unit change in the predictor. The resulting statistic is based upon comparing observed frequencies with the predicted model. When the predictor variable is categorical the odds ratio is easier to explain. This is referred to as the likelihood ratio Field, 2018, pg. 614) 

There are two very different approaches to answering the goodness of fit question. One is to get a statistic that measures how well you can predict the dependent variable based on the independent variables. These kinds of statistics are referred to as measures of predictive power. Typically, they vary between 0 and 1, with 0 meaning no predictive power whatsoever and 1 meaning perfect predictions. The other approach to evaluating model fit is to compute a goodness-of-fit statistic. Ordinarily the deviance can be calculated using the Pearson chi-square test. This formally tests of the null hypothesis that the fitted model is correct, and their output is a p value, a number between 0 and 1 with higher values indicating a better fit. In this case, a p value below some specified α level (say, .05) would indicate that the model is not acceptable. 

Classic GOF tests are readily available for logistic regression when the data can be aggregated or grouped into unique categories. Categories (profile) are groups of cases that have exactly the same values on the predictors. There are two well-known statistics for comparing the observed number with the expected number: the deviance (log likelihood) and Pearson’s chi-square. It’s only when you suppress interactions or non-linearities that the link function becomes an issue. When the outcome is categorical as it is in the model conducted by Malmendier and Tate (2008) this issue occurs. One way around it is to transform the data (Field, 2018, pg. 643). Logistic regression uses transformation to express the linear model equation in logarithmic terms, in so doing allow them to predict categorical outcomes using a standard linear model. In linear models these parameters are typically estimated using the least squares method whereas in logistic regression log likelihood estimation is used (Field, 2018, pg. 643) , which selects coefficients that make the observed values most likely to have occurred, thus log-likelihood is similar to R2 which is the squared Pearson’s correlation between the observed values of the outcome and the values predicted by the model.