It's probably not as simple as you might think.   An excellent resource for mixed models in SAS is https://www.sas.com/store/books/categories/usage-and-reference/sas-for-mixed-models-second-edition/prodBK_59882_en.html   I suggest that you attempt writing code yourself after studying this text. If you then have questions or problems, you can post your code and either your data set or an example data set. Someone in the Community may be able to help then.  ... View more

I would benefit from more detail (like code and example data). I'm not sure how the "where" restriction fits in. If it's a mixed model, then you might want to consider random coefficients. Until more detail is available...   If you incorporate visits as continuous then (by default and depending on details), you are fitting a linear regression of the outcome on visit. This would be a somewhat crude assessment of trend that assumes linearity. Of course, with only 3 visits, it could be hard to assess the validity of the linearity assumption, and a "crude" assessment might just fine. I've taken this approach before and been comfortable with it.   You might find the SAS Statistical Procedures to be a better forum for this question. I have the (recently acquired) power to move your post, but I've never done that before. Let me know if you'd like me to (try to) move it 🙂   ... View more

You could write a contrast for the levels of Occurrence that compares level 0 (non-incident disease group) to the mean of levels 1 and 2 (incident disease groups). ... View more

Returning to the question of analysis of your study...   Based on what I've gleaned, my preference would be for a model in which the number of questionnaires completed is the response. Now I'm thinking about Poisson versus binomial distribution. In a previous response, you imply that the number of questionnaires completed ranges from 1 to 12. How many attempted questionnaires were there (i.e., what was the maximum number of questionnaires that could be completed), and was that number the same for all participants?   ... View more

Oh, how I hated CATMOD. I'm so much happier in the GLM framework 🙂 ... View more

Comment 1: Ah, definitions! Yes, I think we are using two different ones.   McCullagh and Nelder (1989, pp 193-194) take a broad view of the log-linear model, which they define as   log (mu_i) = eta_i = beta^T x_i    i = 1, ..., n   (eq 6.2)   where beta^T is beta transpose. (See the attached pdf for a prettier rendition.) They say, "All log-linear models have the form (6.2). Variety is created by different forms of model matrices; there is an obvious analogy with analysis-of-variance and linear regression models."    On the other hand, Lindsey (1997, Applying Generalized Linear Models) appears to define a log-linear model in the more narrow sense, as does your link https://onlinecourses.science.psu.edu/stat504/node/117 .   I agree, many references to "log-linear model" are in the context of a contingency table and make a distinction between (1) having no variable that serves as a response ("log-linear model") and (2) having one variable serve as a response ("logit model").    I think a log-linear model for a contingency table having no distinction between response and explanatory variables (case (1) above) could be seen as having log(mu_i) = log(cellcount_i) in eq 6.2   Comment 2: I agree, the call to PROC FREQ does create a contingency table.    Is it a contingency table that I would want to analyze? For example, would there be problems with sparseness? Primarily though, I see the number of questionnaires as a response, although I also see that could be arguable. ... View more

Sloppy thinking and writing on my part, my apologies. I'll try to be more coherent, starting with: Any linear model with a log link (or a log transformation of the response) is a log-linear model. Contingency tables can be analyzed as log-linear models, but not all log-linear models are framed as contingency tables.   Thinking more about a contingency table: I'm considering a table cross-tabulated by age (young/old), treatment (yes/no), and color (white/non-white). I would be able to allocate each participant to one of the eight cells. If the experiment was balanced, then all eight cell counts would be equal. Now, what do I do with the value (i.e., the number of questionnaires) associated with each participant? I would not want to fill each cell with the sum of number of questionnaires over the participants belonging to the cell; that would violate the independence of counts assumption. Perhaps I am not being creative enough, but it seems more straightforward to move to a non-contingency-table model. It's possible that the number of questionnaires could be compatible with a Poisson distribution (hence, the model would be a log-linear model, given the log link for the Poisson; also called a Poisson regression model). Of course, I don't have all the details, but my guess is that a binomial distribution might be better because the number of questionnaires theoretically has an upper bound (i.e., the number of attempted questionnaires)--but the binomial approach would require knowing what the number of attempted questionnaires was for each participant.   Does that make sense, or am I overlooking a critical element?   ... View more

The comments by @PaigeMiller and @Ksharp inspired a new thought:   Although a person can fit a loglinear model with a Poisson distribution, in your study I don't think a loglinear model is appropriate. Yes, you have categorical predictors, but you can't build a contingency table with your observations.    I would consider an "ANOVA-like" model using a generalized linear (mixed) model. I doubt that the Poisson distribution is appropriate for these data because the number of questionnaires completed is bounded at the upper end by the number of questionnaires attempted, and the number completed does not appear (from your snippet of data) to be small (for example, zero or one) and may approach the number attempted. Instead I would consider analyzing the proportion of questionnaires completed (number collected out of number attempted) as a binomial distribution, if that makes sense and "number attempted" exists. ... View more

The log-linear model and the Poisson distribution are certainly compatible, but the relationship is not really intuitive for most of us, so you'll have to put in some study to see your way clear. Consult http://data.princeton.edu/wws509/notes/c4.pdf or any other text on categorical data analysis (e.g., Agresti).   "Poisson distribution" and "Poisson regression" are not always the same thing. The jargon is confusing and inconsistent, in my opinion. I like to think that Poisson regression applies to a scenario where you are analyzing a rate by using an offset, but I could also see a generalized linear model (which is a regression model) with a Poisson distribution as being a Poisson regression.   ... View more

When you change the reference class, you are specifying a different parameterization for the same model. Hence, neither is wrong, both are correct, you just need to understand how the coding system determines the definitions of the odds ratios. By studying this SAS documentation, you will be able to sort it out  https://support.sas.com/documentation/cdl/en/statug/63347/HTML/default/viewer.htm#statug_logistic_sect041.htm   This might also help https://stats.idre.ucla.edu/sas/faq/in-proc-logistic-why-arent-the-coefficients-consistent-with-the-odds-ratios/   ... View more

An excellent resource for the MIXED (not "MIX") procedure is  https://www.sas.com/store/books/categories/usage-and-reference/sas-for-mixed-models-second-edition/prodBK_59882_en.html    I suggest that you first make an effort at the code yourself. If you have questions after that, then you can post your code, a detailed description of your study, and an example data set.   ... View more