Also it looks like you have overdispersion which isn't uncommon with Poisson (deviance value/df in output equals ~ 60). This value should be around 1. This could be due to a number of things... missing important predictor variables in the model, outliers in the data, positive correlation between responses if working with clustered data. Whatever the cause, it's throwing off your standard errors and type III test results ultimately increasing type I error. Try using negative binomial. Change dist=negbin, keep the rest of your code the same, and re-run. At the bottom of the Analysis of ML Parameter Estimates output table there will be an estimated dispersion parameter. If this value is significantly greater than 0, it confirms overdispersion in your original Poisson model. Re-check the deviance value/df to see if the dispersion parameter from the negbin distribution helped accommodate the excess variability. If not, consider researching the PSCALE and DSCALE options in the MODEL statement to adjust the standard errors and/or revisit your data to determine potential root cause(s).
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