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I have a dependent variable being positive, discrete (number of people migrated) and the independent variables are all continuous. I want to study the impact of the independent variables on the dependent one to see what factors are shaping migration. The independent variable and some of the independent ones are heavily positively skewed (skewness around 4, QQ plot does not indicate normality). Also, correlation between predictor variables is present (colinerarity). These reasons led me to choose a GLM poisson regression with the log link function SAS using proc genmod.

I have two questions:

  1. Why is deviance 0 and Pearson Chi-Square missing in the below output? Does this mean the model is not suitable for the data? If yes, what tests do exist to find out what model is suitable.

enter image description here

  1. In the Parameter Estimation output, some of my variables are shown as highly significant (Pr>ChiSq of <.0001), even if they not correlated with the dependent variable using a simple (Pearson) correlation. Should I be concerned or am I comparing two different things?

Note: when running an OLS regression, none of the variables is shown as highly significant. What model should I believe?

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  • $\begingroup$ How many variables do you have? $\endgroup$
    – gung - Reinstate Monica
    Jul 7, 2021 at 17:10
  • $\begingroup$ I have 40 variables. A lot of them redundant. I removed the correlated variables, used negative binomial model instead of poisson and I got better results (deviance 1.5). But depending on what variable I add or remove, the parameter significance changes – $\endgroup$
    – Charlotte
    Jul 8, 2021 at 13:22

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The deviance is 0 because the model perfectly fits the data. Your model is staturated (see: What is a “saturated” model?). You have more variables (40) than data (27).

Because you have missing data for some of your variables, and because SAS is using complete case analysis by default (only using those observations that don't have any missing data on any of your vairables), you are losing most of your data. You have presented two tables. If you look at the top one, it shows that you started with 171 data, but 144 have missing values somewhere. Thus, you end up using only 27.

Because your model is staturated, you get perfect predictions. That is, every datapoint is exactly fit by the model. Thus, when the deviance (a measure of lack of fit) is calculated, it's 0. As a result (although the connection is unlikely to be obvious to you), there is no way for the model to estimate the amount of inherent noise in the system to use for conducting statistical tests. Thus, the tests (e.g., Pearson's chi-squared) are missing.

There are ways to get estimates when you have more variables than data, and there are more sophisticated ways to deal with missing data, but both are very complicated. I suggest you work with a statistical consultant.

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  • $\begingroup$ I learned so much! thank you! $\endgroup$
    – Charlotte
    Jul 9, 2021 at 15:50
  • $\begingroup$ You're welcome, @Charlotte. $\endgroup$
    – gung - Reinstate Monica
    Jul 9, 2021 at 15:51

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