Dear Steve, I am very sorry for the late answer to your comment, but I was "out of commission" for a few days. Some covid scare and things like that. Thank you for your very educational, tactful, and wise answer. You are really very good at explaining concepts. I say this because I have seen your answers to many other questions in this forum. I want to clarify that I only want to know what treatment increases fecundity when interacting with time. A simple ls-means table of Treat*Time would be enough for me. I do not want to predict anything. Given the above, I have two questions: 1) Is it better to always go with a "simpler" covariance structure, as long as the results are similar to those obtained when running models with more complex covariance structures? 2) are there considerations that may force me to go for a more "complicate" structure? See below to understand my train of thought. According to "Stroup et al. 2018. SAS for Mixed Models. Introduction and basic Applications", it seems that AR(1) is a good simple structure for most cases (if non-negligible distance dependent within-subject correlation exists, switching from CS to AR(1) accomplishes the first 90% for accounting for within-subject correlation as a function of distance apart in time). That said, the evaluation of the different covariance structures for my model shows the following: It seems that ARH(1) is better than AR(1). AR(1), as "simple" as it is, it has a large residual. Take a look at these two fit statistics for AR(1). Generalized Chi-Square 4830671 Gener. Chi-Square / DF 7958.27 ARH(1) has better values for these two: Generalized Chi-Square 618.88 Gener. Chi-Square / DF 1.02 However, the more complex ANTE(1) seems to be even better than the two above, judging by the AIC, AICC, BIC and log likelihood values below: Fit Statistics -2 Res Log Likelihood 6977.15 AIC (smaller is better) 7021.15 AICC (smaller is better) 7022.88 BIC (smaller is better) 7046.13 Generalized Chi-Square 619.29 Gener. Chi-Square / DF 1.02 Technically, ARH(1) and ANTE(1) are better than AR(1), and ANTE(1) is the best of all. The model with AR(1) shows that the interaction Treat*Time is significant (this is my main question). This interaction is also significant with models with ARH(1) and ANTE(1). Is it fine if I run my final model with an AR(1) covariance structure (simpler structure, but high residual variability)? Thank you in advance for your help. Regards, marcel ... View more

I wanted to make it clear that that I found a solution to my question from two members' comments: 1) paigeMiller and 2) sld. I just do not know how to accept two sources as part of a single solution. Sorry about this.   regards,   marcfel ... View more

sld,   Very insightful observations and thank you for sharing your experience with me. I appreciate it very much. I was worried about the Bonferroni adjustment for 300 comparisons. Your advice with respect to this issue is timely.   I will run a few LSMESTIMATE contrasts with my data. I will check the pdf you suggest me to read.   Regards,   marcel ... View more

sld,   That is a beautiful graph. That was one of my headaches, how to plot the logistic interactions in sas. Thank you very much. For me, is ts hard to customize sas graphs. I will use the sas output to customize a graph in excel.   As per lsmeans vs slice, I see that lsmeans produces pairwise comparisons that slice does not (at least by running the sas codes I used for my examples). The thing is that my code for lsmeans produces 300 pairwise comparisons, and the bon adjustment of the P values reflects that, with most of the adj P values being 1. The adj P values are lower when using slice than when using lsmeans. If there would be a way to make lsmeans compare sets of 10 pairs, it would be helpful.   I am also interested to know if my interpretation of lsmeans for the main effects and slice for the interactions is correct. Could you please take a look at the rtf files attached to my previous reply? If you have the time, of course.   Regards,   marcel ... View more

I followed this note to explore the use of lsmeans.   I used slice to explore the interactions, instead of lsmeans. They produce practically the same output. But, lsmeans produces 300 pairwise comparisons and the adj P values are mostly 1s. Slice produces smaller sets of pairwise comparisons. However, I see the advantages of using one or the other.   I think this is better visualized the .rtf file attached, because I highlighted the comparisons. Please, see the attached file.   Ex. lsmeans Bact*Sick / diff oddsratio cl adjust=bon; Bact Sick _Bact _Sick Estimate Standard Error z Value Pr > |z| Adj P Alpha Lower Upper Adj Lower Adj Upper Odds Ratio Lower Confidence Limit for Odds Ratio Upper Confidence Limit for Odds Ratio Adj Lower Adj Upper Odds Ratio Odds Ratio E Z E W -2.9256 1.4712 -1.99 0.0467 1 0.05 -5.8091 -0.04219 -8.4644 2.6131 0.054 0.003 0.959 <0.001 13.641 E Z E Y -1.1096 1.6488 -0.67 0.501 1 0.05 -4.3412 2.122 -7.317 5.0978 0.33 0.013 8.348 <0.001 163.664 E Z E X -3.4508 1.4564 -2.37 0.0178 1 0.05 -6.3053 -0.5963 -8.9339 2.0323 0.032 0.002 0.551 <0.001 7.632 E Z E V 2.00E-15 2.0165 0 1 1 0.05 -3.9523 3.9523 -7.5918 7.5918 1 0.019 52.054 <0.001 >999.999 E W E Y 1.816 0.9036 2.01 0.0445 1 0.05 0.04492 3.5872 -1.586 5.2181 6.147 1.046 36.131 0.205 184.587 E W E X -0.5251 0.4681 -1.12 0.262 1 0.05 -1.4427 0.3924 -2.2876 1.2373 0.591 0.236 1.481 0.102 3.446 E W E V 2.9256 1.4712 1.99 0.0467 1 0.05 0.04219 5.8091 -2.6131 8.4644 18.646 1.043 333.317 0.073 >999.999 E Y E X -2.3412 0.8794 -2.66 0.0078 1 0.05 -4.0647 -0.6176 -5.6519 0.9695 0.096 0.017 0.539 0.004 2.637 E Y E V 1.1096 1.6488 0.67 0.501 1 0.05 -2.122 4.3412 -5.0978 7.317 3.033 0.12 76.798 0.006 >999.999 E X E V 3.4508 1.4564 2.37 0.0178 1 0.05 0.5963 6.3053 -2.0323 8.9339 31.525 1.815 547.45 0.131 >999.999 slice Bact*Sick / sliceby=Bact diff oddsratio cl adjust=bon;   Slice Sick _Sick Estimate Standard Error z Value Pr > |z| Adj P Alpha Lower Upper Adj Lower Adj Upper Odds Ratio Lower Confidence Limit for Odds Ratio Upper Confidence Limit for Odds Ratio Adj Lower Adj Upper Odds Ratio Odds Ratio Bact E Z W -2.9256 1.4712 -1.99 0.0467 0.4674 0.05 -5.8091 -0.04219 -7.0553 1.204 0.054 0.003 0.959 <0.001 3.333 Bact E Z Y -1.1096 1.6488 -0.67 0.501 1 0.05 -4.3412 2.122 -5.7378 3.5186 0.33 0.013 8.348 0.003 33.738 Bact E Z X -3.4508 1.4564 -2.37 0.0178 0.1782 0.05 -6.3053 -0.5963 -7.5389 0.6374 0.032 0.002 0.551 <0.001 1.891 Bact E Z V 6.66E-16 2.0165 0 1 1 0.05 -3.9523 3.9523 -5.6604 5.6604 1 0.019 52.054 0.003 287.264 Bact E W Y 1.816 0.9036 2.01 0.0445 0.4447 0.05 0.04492 3.5872 -0.7205 4.3526 6.147 1.046 36.131 0.486 77.681 Bact E W X -0.5251 0.4681 -1.12 0.262 1 0.05 -1.4427 0.3924 -1.8392 0.7889 0.591 0.236 1.481 0.159 2.201 Bact E W V 2.9256 1.4712 1.99 0.0467 0.4674 0.05 0.04219 5.8091 -1.204 7.0553 18.646 1.043 333.317 0.3 >999.999 Bact E Y X -2.3412 0.8794 -2.66 0.0078 0.0776 0.05 -4.0647 -0.6176 -4.8096 0.1273 0.096 0.017 0.539 0.008 1.136 Bact E Y V 1.1096 1.6488 0.67 0.501 1 0.05 -2.122 4.3412 -3.5186 5.7378 3.033 0.12 76.798 0.03 310.387 Bact E X V 3.4508 1.4564 2.37 0.0178 0.1782 0.05 0.5963 6.3053 -0.6374 7.5389 31.525 1.815 547.45 0.529 >999.999 Thank you for your help;   marcel ... View more

Following PaigeMiller's advice, I looked into the use of lsmeans to explore the interactions in the logistic regression. I am attaching two .rtf files showing my interpretation of the results and some doubts I have about it. The messages would be too long to show them in a normal message window. Please, would any of you kindly take a look at my files and provide me with your expert advice? Regards, marcel ... View more

PageMiller,   Thank you for your answer. The excel file also shows the SAS code (abbreviated version), the Chi^2 test, and the class level information produced by sas. It also shows a summary of the success of infections from actual data from my experiment.   I will check the LSMEANS for categorical variables. This seems to be getting more and more and more and more complicated. I hope I am not choosing to take the red pill. I am really a novice at the logistic.   Thank you,   marcel ... View more

Dear PaigeMiller,   You are suggesting that the basic idea on interpreting categorical interactions expressed in the rtf file is not correct. If that is the case, then I need help to correctly interpret those interactions.   To restate my question: I can't figure out how to interpret the coefficients for the interactions. Do you have any suggestion on a decent and easy to read (for the non-expert) literature on the topic?    Thank you.   Marcel ... View more

Here is the code   ods graphics on/imagemap ; proc logistic data=data1 class Bact (param=ref ref="A") Sick (param=ref ref="V") ; model Event/Trials = Sick Bact Sick*Bact /expb scale=none link=logit lackfit firth clodds=pl; ods output cloddspl=firth; id idor; run; ods graphics off;     Thank you for your help ... View more