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How can I evaluate which model - between linear and logit - determine the best fit to the data? The models use the same input variables and I thought that comparing the deviances was the proper choice but in my case I get a lower deviance in linear model (wasn't it supposed to be higher). What am I supposed to use to compare these models? Here the results:

#LINEAR
Null deviance: 178568  on 1107865  degrees of freedom 
Residual deviance: 163398  on 1107820  degrees of freedom
AIC: 1023626
#LOGIT
Null deviance: 1114802  on 1107865  degrees of freedom
Residual deviance: 1017671  on 1107820  degrees of freedom
AIC: 1017763
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    $\begingroup$ Welcome to Cross Validated! What exactly do you want to do? // If you're using linear regression, you probably assume a Gaussian likelihood, meaning that you are comparing a measure of square loss and a measure of log loss. $\endgroup$
    – Dave
    Commented May 6, 2022 at 16:13
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    $\begingroup$ You don't mention what the outcome variable is, which tends to be the most important consideration in choosing between a linear regression (used to model continuous Y) and logistic regression (used to model counts). $\endgroup$
    – dipetkov
    Commented May 6, 2022 at 16:51
  • $\begingroup$ The outcome is a binary variable, which makes logit model clearly the proper choice, as far as I have studied. But I need an estimator of goodness of fit in order to get a numerical proof that logit is superior than linear. I know that logit is explicitly developed to fit binary outcome, but what if I wanted to get the numerical proof in terms of goodness of fit (compared to linear model)? $\endgroup$
    – StefanoB
    Commented May 6, 2022 at 17:02
  • $\begingroup$ Your linear deviance is actually higher ? Also, a linear regression is used for regression and logistic regression is used for classification, those models aim different goals. $\endgroup$
    – Lelouch
    Commented May 6, 2022 at 20:25
  • $\begingroup$ You simply cannot compare deviance between linear and logistic regression, as hinted at in the other comments. See stats.stackexchange.com/questions/345069/…, $\endgroup$
    – kjetil b halvorsen ♦
    Commented May 7, 2022 at 1:04

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