Hello All,
I have tried to organize the results so that you can easily understand what I am trying to ask. I would like to provide you my results in word file which I have attached here.
Big picture curiosity: I am not being to figure out why there is no consistency between glm () function output and anova () function output which is based on the model fitted into the data by glm () function.
My questions are as follows: (Please look at word file to see the model number)
1. The output from model 1 (A) and model 4 (D) did not show any significant effect of any sub-levels of independent variable on dependent variable. However, when I used anova () function for chi-square test based on aforementioned models, independent variable "Days" is significant in each test. I believe this should not happen. What do you think?
2. When I removed the intercept from model 3 (C) using "-1" in the glm () function, then the output from model 3 (C) showed significant effect of sub-levels (E75 and E99) of "Storage" but I did not observe any significant effect of sub-levels of "Days" independent variable on dependent variable. However, when I used anova () function for chi-square test both independent variable (Storage and Days) was significant. How is it possible?
3. Model 6 (F) is manipulation of model 5 (E), and model 8 (H) is manipulation of model 5 (G). The only difference between them in glm function () is "-1". The result of significance is different. Which are the better models?, and which model should I use?
You have a model with estimated coefficients. This is one thing. Testing the deviance-reduction by individual factors of nested models is another thing.
The p-values in the coefficients table are from z-Tests of the estimates.
The p.values in the ANOVA table are from a whole series of comparison of the deviances of two models. The first p-value is comparing Y~Storage vs. Y~1, the second is comparing Y~Storage+Days vs. Y~Storage, and the last is comparing Y~storage+Days+Sorage:Days vs.Y~storage+Days.
The question that is answered by the coefficients table and by the ANOVA table is different, and so it is not surprising that the answers are different. This answer should help you clarify your points 1 to 3. Hopefully :)
Further to Jochen's answer there are (at least) two main ways to get p values for a test of a single parameter in a logistic regression:
- the Wald test computed as estimate/SE (the z test)
- the likelihood ratio test (a difference of maximised likelihoods between models with and without a parameter)
Even when the tests match the two methods don't necessarily agree (except asymptotically). Generally the LRT approach is more accurate.
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