Generalized Regression Personality and Diagnostic Bundle

Question

Hi All,

I have a quick question; JMP13 pro comes with a Generalized Regression personality.  After fitting the data, it is possible to check the residuals using the Diagnostic Bundle.  Are the residuals to follow the ANOVA assumptions (i.e. normality, homogeneiety, iid) if I use the Gamma Distribution?

Thank you

Generalized Regression with Gamma Distribution

Mark_Bailey · Answer

The variance is proportional to the response level. You might try a Poisson log-linear regression through the Generalized Linear Models personality since you are counting. Select the Poisson distribution and the canonical log link function. Be sure to include both options: over-dispersion and Firth bias adjustment. Because you are using a DOE, I expect that the opportunity for each run is the same and, therefore, no offset is required.

rs · Answer

I am trying to address if the treatments, fungicide type (X1) and fungus batch (X2), affect the average number of spores (Y).  The experimental design is a 2x2 factorial with 4 replicates per treatment combination.  The analysis of the residuals do not meet the ANOVA assumptions.  In particular, I am concerned that the residuals do not appear normally distributed and have unequal variances, therefore invalidating the conclusions of statistical significance of the treatments.

Transforming the data does not ‘normalize’ the residuals either.  Therefore, I am interested in applying any distributions (such as Gamma) that Generalized Regression personality in JMP offers.

Peter_Bartell · Answer

Before we get too much further, rather than discuss the residuals, perhaps you can share with us the practical problem you are trying to address? In your file you have a nice balanced, replicated designed experiment with two nominal factors at two levels each. With 4 replicates per treatment combination. One rarely creates a design such as this without some forethought and rationale. Before I start examining 'statistics' and visualizations to evaluate a study that someone else created, I'd like to understand the goal of the study.