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I have the Ramsey's reset test result to find whether my regression has any omitted variable bias. It is based on the logistic regresison model which is a non-linear model. I have the following result and shall I say I do or do not have omitted variable bias and why?

   > resettest(reg_logit,power = 2,type="fitted", data=DATA)

      RESET test

   data:  reg_logit
   RESET = 1.8529, df1 = 1, df2 = 3273, p-value = 0.1735

But when I run this ramsey test without any specification on this same logistic regression, I get the result as follows:

   > resettest(reg_logit)

           RESET test

   data:  reg_logit
   RESET = 19.748, df1 = 2, df2 = 3272, p-value = 2.983e-09
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Based on the lmtest package manual, you appear to have five continuous predictors (and maybe some categorical predictors) in your model. We know there are five continuous predictors because your first degrees of freedom is 5, and you can only add squared continuous variables to a model, not squared dummy variables as stated in the manual.

These predictors were squared (power = 2) and added to the original model to create a new model. And an F-test was used to compare your original model to this new model. The F-test was statistically significant suggesting that at least one of the squared continuous predictors is a statistically significant predictor of your outcome.

Your second degrees of freedom is large, so you have a huge sample size, large enough to detect even trivial effects. Even if the relationship is slightly quadratic, you have the power to detect it. Without an explanation of the context, access to the coefficients, some diagnostic plots, one cannot know how problematic your misspecification is.

Note that the RESET test is a test for functional form specification not omitted variable bias (OVB). And OVB might affect some variables while others are not affected. The simplest answer to your question about OVB is yes, it is present. Since you have multiple predictors and individuals were most likely not randomized to have those values of the predictors, there will be OVB.

The package manual and Wikipedia do a decent job of explaining the test. Section 6.2.3 of Wooldridge's Econometric analysis of cross section and panel data (2010) clarifies what the RESET test is and misconceptions about it like its (in)ability to test for OVB.

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  • $\begingroup$ The data size is large which is 20383. If so what would you say about the omitted variable bias in this case? I also changed the result output as well by having a more simplified example to investigate and figure out the omitted variable problem. $\endgroup$ – Eric Nov 13 '18 at 17:03
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    $\begingroup$ I already know the dataset is large. There is no definitive test for omitted variable bias. Like I wrote in the reply, unless your participants were randomly assigned to their values on the predictors, you have omitted variable bias. $\endgroup$ – Heteroskedastic Jim Nov 13 '18 at 17:06
  • $\begingroup$ If I use the type as "fitted" or "princomp" instead of "regressor", it shows insignificant P-value aligned with my purpose. Can I do in this manner then? $\endgroup$ – Eric Apr 14 at 14:37
  • $\begingroup$ Selecting what the analysis you want based on how desirable the p-value is makes the p-value meaningless. Better yet, try to understand why the results change in the way they do. $\endgroup$ – Heteroskedastic Jim Apr 14 at 14:44
  • $\begingroup$ It's because I am using a logistic regression, a non-linear model, which I think to be the reason. So I think "fitted" works better in this case. If so, shall I presume no omitted variable bias? I just updated my results and the data + model are even different from before. $\endgroup$ – Eric Apr 14 at 15:02

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