I am running a multivariate logistic regression to predict the likelihood of individuals voting for the green party, using a survey of european election studies of 2019. My main IV is education levels; when I add other explanatory variables, there are significant. However, my classification table (as shown below) shows that my model cannot predict anything; I have tried using other IVs to see if that could be the issue but, as I thought, it is not. I do not know how to resolve it; or can I simply state in my report that the goodness of fit of the model is simply not so good?
I would like to understand why this is happening and if there is a way for me to resolve it?
Katia,
First, check to make sure you are looking at the "second" classification table with all variables in the model. SPSS has a silly (in my opinion) habit of including the classification results including no variables in the model for the first table in its LR routine.
My best,
John
Also, for (sadly) low frequency events (at least outside of Brighton! Yea Caroline Lucas! … I used to live there), even adding lots of predictive variables will not make a low baseline probability event be estimated about 50%. For example, if you were predicting Tornadoes you would say everyday next year there will not be a tornado (this is the historical example given about a century ago for why percentage accurate is a bad measure for most situations). The classification tables are not a good way to judge the fit of a model.
This is not answering you question directly, but I would like to point out that there is a problem in using standard logit models when the number of cases for one outcome is relatively rare compared to the other. It is often a problem in voting data, and in disease etiology. And it is the absolute number that counts. The usual maximum likelihood estimates are known to be biased.
This is a good and clear account of the problem and suggested solution (Firth logistic regression). https://www3.nd.edu/~rwilliam/stats3/RareEvents.pdf .This is also a good account followed by illuminating questions and answers:
https://statisticalhorizons.com/logistic-regression-for-rare-events
For users with IBM SPSS Statistics version 23 or higher, the STATS FIRTHLOG extension is installed as part of IBM SPSS Statistics-Essentials for R. For Stata see Article FIRTHLOGIT: Stata module to calculate bias reduction in logi...
and for R see https://cran.r-project.org/web/packages/logistf/logistf.pdf
That of course is tackling the problem via analysis, it is also possible to do ameliorate at the design stage by oversampling the 'cases' (with or without matching). That is sampling on the outcome.This is often used by epidemiologists in what is known as a case: control design. While, you cannot use the data to estimate prevalence as you have fixed this, ( eg 50 cases and 50 controls; or 50 cases and 200 controls ) but under certain assumptions you can get regression-like estimates of the effect of exposures on the outcome. ( See Book Epidemiology: An Introduction
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