3
$\begingroup$

My predictions are far off the actual values, and I really do not understand what I am doing wrong. I have 20 dummy independent variables, and a continuous dependent variable. The dataset is small, 1000 points approx. The best result I got so far is using generalized linear regression, Poisson link function, and include all interactions terms. Only after introducing interactions terms, I actually find that some (less than 50%) of my prediction actually somewhat follow the true value. What else could I be missing to explain the remaining data? Could it be that simply my independent variables are not good predictors for the remaining part of the data?

Below I show you the predicted (y) vs observed (x) dependent variable, the residuals (y) vs actual dependent variable (x), and the residual (y) vs the predicted dependent variable (x). enter image description here

$\endgroup$
5
  • 2
    $\begingroup$ (1) Look at the model you obtain when you remove that outlier (with an outcome of 1.0). (2) Consider a different model designed to handle the evident discrete nature of the outcome (it focuses on particular values near 0, 0.19, and 0.38). $\endgroup$
    – whuber
    Mar 10 '17 at 15:54
  • $\begingroup$ As well as @whuber suggestions you need to consider that you have some points in sparsely populated areas of the space of the X's. Your residual plot does not look that bad to me, modulo the point with large negative residual. $\endgroup$
    – mdewey
    Mar 10 '17 at 16:03
  • $\begingroup$ @mdewey, why do you say it does not look bad? To me the simplest plot to interpret is the second, that shows that if the "true" relation was y= x, I am really predicting something like y=0.5. That is a large bias. $\endgroup$
    – famargar
    Mar 10 '17 at 16:11
  • $\begingroup$ Sorry, I meant the third plot, the conventional one for examining the assumptions, not the second one. $\endgroup$
    – mdewey
    Mar 10 '17 at 16:13
  • $\begingroup$ I guess I do not understand well the third plot. Sure enough, the model as is is clearly wrong, unless one is willing to calibrate it using the middle plot. BTW, I edited the question to remove the outliers. I can only see the same mess, but closer :( $\endgroup$
    – famargar
    Mar 10 '17 at 16:15
1
$\begingroup$

The third plot is the most useful. Your data is showing heteroskedasticity, that is, the variance of the error term is not constant. It is clear by the third plot. Your error should be randomly distributed around zero. The others plots are not very useful to me at this point. Plot $\sqrt{\hat{e}}$ (e is the error) vs $\hat{y}$ too and check it. I suggest to use Generalized LS estimator, or try a transformation of $y$, either log or Cox transformation.

$\endgroup$
1
  • $\begingroup$ Thanks Diogo. Please see my new edit: basically going from OLS to GLM (did you mean to say Generalized Linear Model, or something else) did not change the outcome. Adding interaction terms now does a bit of explaining the data. However, a good fraction of the data still has no good model! $\endgroup$
    – famargar
    Mar 20 '17 at 10:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.