Thanks for sharing good resources. When I read this article, it says they did some overdispersion correction to account for heteroscedasticity which takes care of different levels of dispersion in the model on page 23/45. I wonder if this is possible in the following SAS code. It appears that the article is not talking about SAS codes.   proc glimmix data=dissertation1 plots=(studentpanel boxplot(fixed student)); class subjectid group slc ; model Hamm_Par_syl_ver4= group|slc/solution dist=gamma; output out=preddata pred=pred resid=r; random intercept /*slc*/ / subject=subjectid(group) ; /*random _residual_ / group=slc;*/ lsmeans group*slc / plot=meanplot(sliceby=group join cl); slice group*slc / sliceby=group diff alpha=.0083; slice group*slc / sliceby=slc diff alpha=.0083; lsmeans slc/diff alpha=.0167; lsmeans group/diff alpha=.025; lsmestimate group*slc "Group effect: SLC 1 v 2" 1 -1 0 -1 1 0, "Group effect: SLC 1 v 3" 1 0 -1 -1 0 1, "Group effect: SLC 2 v 3" 0 1 -1 0-1 1 / adjust=simulate(seed=29847); run;   Thanks for your advice in advance. ... View more

I see. That is good to know. So I will then report what appears as estimate as the difference value between two conditions rather than pure mean value I obtained from descriptive stat.   I learn a lot from you. Thank you very much again!     ... View more

I see your point. I came to ask different question, because the estimate value was different from what I obtained as difference value between two means from the descriptive stat table. Now, I have to admit how little I know about all these tools. I have no idea what that estimate is estimating.   Thanks for your advice in advance.     ... View more

  Thank you. You mentioned that I can calculate the difference by hand, but I thought I could read in the difference from the estimate column. For example, the DV in phase_info1=1 is higher by 0.4988 than phase_info 1=2. Was I wrong?   Thanks for your advice in advance. ... View more

Thanks for sharing good resources to learn those models.   Now, I am considering whether proving any violation of linearity assumption in the variance would be a sufficient assumption test for variance aspect of the GLMM with non-normal distribution.   Thanks for your advice in advance.   ... View more

Thank you again, Sid. Yes, the model includes phase_info1, Phoneme_stress, and phase_info1 * Phoneme_stress in the final equation in both fixed and random effects, because phase_info1 and Phoneme_stress are all first level variables and I am interested in the interaction of these two variables.  And no, my dependent variable is just an error measurement from acoustic signal, so it is nothing to do with stat analysis. Thanks for checking.   Please let me know if anything else can be a problem. Thank you!   ... View more

After exploring a little bit, I found following two codes worked.   data a1.prediss1; set a1.prediss; where Error=0 And (Phoneme_stress in (0, 1)); run; data a1.Prediss1; set a1.Prediss; where error=0; if Phoneme_stress in (2, 3, 4, 5) then delete; run;   I wanted to include only Error=0. Error is a dichotomous variable. ... View more

I wanted to included only error=0 values in all those conditions I wanted to include (phoneme_stress=0 or 1).   Does it change any of the codes I created or received from Reeza?   ... View more

Thank you. ... View more

Thanks for your advice and all of your explanations. Could you recommend me any book to learn more about GLM and GLMM?   Here are my responses: 1. If I understood your note correctly, as long as I assume GLM that has non-normal distribution, I do not need to assess normal distribution. Also, GLMM is an extension of GLM, if I go with GLMM with gamma distribution, I do not need to worry about normal distribution.    In my data set, most of the dependent variables violated normality assumption and I chose gamma distribution for GLMM. So, if I chose GLMM with gamma distribution, I would not need to worry further about normality assumption.   I got this message clearly, but after reading your additional comment about normality test on random effects, I became puzzled again. You mentioned that we do not need to test normality assumption on residuals, but on random effects. How do we test normality assumption on the random effects? I assume there will be several variables included in the random effects in GLMM depending on the model I am testing. I wonder how you compose your SAS code in order to reflect these changes. Or should I dig into more to learn what it really means by random effects?   2. I got the point that I did not need to make adjustment in SAS code assuming this one line 'random _residual_' would take care of the heteroscadasticity problem. That is actually good because the model did not converge when I chose 'gamma' distribution and when I left this one line active. I had to make either one of them deactivated, in order to obtain the results. I also understand that variance of GLM becomes complicated because it is dependent on mean. I also understand that residual tends to be homogeneous in GLM and does not requires homogeneity of variance test (although I did not completely understand what the link scale is.) Does it mean any sort of homogeneity of variance test is unnecessary for GLM or GLMM? If it is still required, on what variable do we test it?   I now know maybe what I did for homoscedasticitiy assumption test on residual might have been unnecessary procedure. After this testing, I had only one dependent variable out of many variables violated this assumption. I still don't know a good way to remedy for this violation in the further analysis. Should I just ignore this violation and run GLMM like usual and say this result is not trustworthy because one of the assumptions was violated?   Thanks for your reply in advance.   ... View more

Here are my answers:   Why did you switch from a normal distribution assumption to a gamma distribution assumption?     I presume that "GMP_log" is a log transformation of GMP. The gamma distribution uses a log link. Is it appropriate to essentially "double up" with a log transformation?   I first did square-root and log tranform for the dependent variable in order to see if the data meets normal distribution assumption. The double up occurred after I found none of these transformed data met the normality assumption. I specified the distribution as gamma in the proc glimmix while I still maintained the transformed DV. I was trying to make the model converge with transformed DV because while the model converged well with gaussian distribution, it did not easily converge with the gamma distribution.     If you specify a distribution other than normal (for example, gamma), why would you choose to test normality of residuals from a generalized linear (mixed) model?   I tested normality assumption first and went to choose gamma distribution later. But, I realize that you pointed out why I tested the normality assumption again after I decided to go with gamma distribution, and I think that is a good point. I was listening to one statistician's advice, and I think he was wrong to advise me to test it one more time. Does this answer your question?   What is the purpose of  random _residual_ / group=phase_info1; and how does that work with a gamma distribution (compared to a normal distribution) and how does it mesh with your desire to assess the distribution of the pooled residuals?   I've learned that in proc glimmix, people replace repeated statement to 'random _residual_' statement. However, I did not use above statement to make this adjustment, but because my data did no meet the homogeneous of variance assumption. So for me, although "phase_info1" really is a repeated variable, this statement was nothing to do with the repeated condition, but to make adjustments for heterogeneity of variance problem. Also, as far as I remember, the statement I used 'random _residual_' statement slided by the condition variable was something I learned from you in another previous thread of mine at sas.com as a remedy for heteroscadasticity problem. As I write here, I think maybe I will need to use above residual value to test homogeneity of variance one more time after I make random _residual_ statement to check whether this statement really ensures this assumption. What do you think? Is there a better remedy than this statement to accommodate for heteroscadasticity problem?   If you have any further questions, please let me know.   If I ask one question about GLM, I am learning that GLM allows to have more distribution options than normal distribution. If I decide to test data in GLMM and choose proc glimmix command, can I just ignore whether data meets normal distribution assumption or not? ... View more

I see why you ask all these questions. I will study GLM and GLMM before I answer your questions. Thanks for your concern and advice! ... View more