If you have the actual event (c section) counts for all the states and the state populations, which presumably are the numerators and denominators of the rates, then I assume the sums of the counts divided by the sums of the populations would equal the 22.5 US rate. In that case, I think what you are looking for is what the DIFF=ANOM option in the LSMEANS statement can provide. This shows an example with such data. Note that the log of the state populations is used as the offset. proc genmod; class state; model cseccount=state / dist=poisson offset=logstpop; lsmeans state / ilink diff=anom; run; An example involving proportions rather than rates can be found in this note.   But if you only have the rates as in your example table, then I guess the best you could do is to treat the US rate as a constant and test each state rate against it. The easiest way to do that is with a set of LSMESTIMATE statements that use the TESTVALUE= option to specify log(22.5) as the comparison value. Note that the LSMESTIMATE statement will compare the ESTIMATE value, which is the log rate, to the TESTVALUE. The following statements do this for the first two states. Note that the states will be in alphabetic order, so AK is first, followed by AL. proc genmod; class state; model strate=state / dist=poisson; lsmestimate state 'AK' 1 / ilink testvalue=%sysfunc(log(22.5)); lsmestimate state 'AL' 0 1 / ilink testvalue=%sysfunc(log(22.5)); run;   ... View more

If, at the subject level, the response is binary (such as yes/no, positive/negative) so that your data are aggregated binary data and you have the numerator and denominator counts making up the proportions, then you can fit a logistic model in procedures such as LOGISTIC, PROBIT, GENMOD, GAM, ADAPTIVEREG and others by using the events/trials syntax in the MODEL statement. The model assumes that the proportions represent a set of independent Bernoulli trials and have a binomial distribution. See the example in the Getting Started section of the PROC LOGISTIC documentation. But if your data are counts of some event over a period of time (such as person-years) such that the ratio of count/time is a rate that can exceed 1, then you would typically model the rate using a Poisson or negative binomial model with the log of the time variable as an offset. See the Poisson Regression example in the Getting Started section of the PROC GENMOD documentation.  ... View more

You might be able to get essentially what you want by using the EFFECT statement in a suitable modeling procedure rather than by using PROC GAM (or the newer and recommended PROC GAMPL). For example, the following fits a model like you describe to the diabetes data in the Getting Started example in the PROC GAM documentation using the EFFECT statement in PROC ORTHOREG. See the description of spline effects using the EFFECT statement in the Shared Concepts and Topics chapter of the SAS/STAT User's Guide. proc orthoreg data=diabetes; effect s1=spline(age/ basis=tpf(nopowers)); model logcp=s1/noint; effectplot; run; ... View more

The significant interaction tells you that the difference in the SES groups changes depending on the distance, or equivalently that the effect of distance depends SES - think of the slope of the two distance curves for the SES levels at each of various values of distance. But note that you are talking about the SES difference or the distance effect in terms of the log odds, not the event probability. This is discussed in more detail in this note. See, in particular, the Poisson model example on rates and the use of the Margins macro at the end which compares the event probabilities at selected values of the continuous predictor (as well as compares slopes). A similar approach can be used for your logistic model. Note also the use of the EFFECTPLOT statement to plot the predicted log odds or predicted probabilities.  ... View more

First, PROC GEE is a newer procedure specifically for fitting the GEE model and is the recommended procedure when fitting that model. Then see this note on specifying the TYPE= correlation structure. As mentioned there, the GEE method is robust to misspecifying the correlation structure, so if you believe that all measurements within STATE are correlated (in varying degrees), you could simply specify SUBJECT=STATE and TYPE=EXCH. That said, the Alternating Logistic Regressions (ALR) method available in PROC GEE (and GENMOD), in which you model the log odds ratio among pairs of measurements, allows nested structures. Using the ALR example in the GENMOD documentation, the following adds a subcluster variable to each cluster with each cluster of size 4 now containing 2 subclusters of size 2. The ALR model allows for two log odds ratios to be estimated - one for within the subclusters and one for between the subclusters. data resp; set resp; if visit in (1,2) then subclusID=1; else subclusID=2; run; proc gee data=resp; class id treatment(ref="P") center(ref="1") sex(ref="M") baseline(ref="0") subclusID; model outcome(event='1')=treatment center sex age baseline / dist=bin; repeated subject=id(center) / logor=nest1 subcluster=subclusID; run; Another alternative approach might be to fit a GEE-like marginal model using PROC GLIMMIX using an appropriate structure. ... View more

The choice of the statistical method most appropriate for your data and goal are up to you, but from what I can tell from your description it sounds as though a Generalized Estimating Equations (GEE) model might be worth considering. If you have multiple measurements of demand over time for each store, you might assume that the measurements within a store are more correlated than measurements between stores. A GEE model allows you to account for correlation within clusters or subjects (stores in your case). See the examples in the PROC GEE documentation in the SAS/STAT User's Guide. You would need to choose an appropriate distribution for your response variable (demand) to be specified in the DIST= option. If this is strictly a positively-valued variable, then the gamma or inverse gaussian distribution is often used, generally paired with the log link function (LINK=LOG option). Note that those two distributions do not allow for zero values. You will also need to choose an correlation structure for the form of the matrix of correlations among the measurements within stores. Since GEE protects against incorrect choice of the structure, simpler structures are often used. The LSMEANS statement can be used to compare the levels of intervention. GIven all of that, the code might look something like this.  proc gee; class store interven; model demand = interven / dist=gamma link=log; repeated subject=store / type=exch; lsmeans interven / diff ilink cl; run; ... View more

If you fit a model using the gamma distribution for the response in the GENMOD, GLIMMIX, or other modeling procedure, then you can probably drop the phrase after the comma. ... View more

What you want can be provided by adding the LSMEANS statement in your GEE step. Since your model involves the interaction of the two predictors, the effect of one of the predictors requires more than just exponentiating that predictor's main effect parameter. It must also involve parameters of the interaction. Also, since each predictor is categorical, there isn't a single estimate of its effect. A predictor's effect is assessed by a set of comparisons among its levels. This is automatically done for you by the LSMEANS statement. The following statement provides, in the Differences tables, the exponentiated comparisons among the levels of one predictor, averaged over the levels of the interacting predictor. The exponentiated estimates are ratios of mean counts. The  E option shows the combination of parameters that are involved in the computation that is exponentiated. The manner in which that averaging is done can be altered by additional options available in the LSMEANS statement - see the documentation of the LSMEANS statement. lsmeans PREPG_CAN_NEW trimester / e diff exp cl;   ... View more

Still not seeing the problem. A zero-inflated variable does not imply that its distribution, whatever it is, has zero mean - it just allows a mass of values at zero. A distribution with non-negative support, like the Tweedie, can't have zero mean, but maybe you want a distribution supporting the real numbers, including negative numbers, with an extra mass at zero exceeding the expectation of the distribution. You might be able to do that in PROC FMM with a degenerate distribution at zero. ... View more

Not sure I see the problem with prediction. While the distribution mean cannot be zero, individual realizations from the distribution can be zero. For instance, the PDF at zero for a Tweedie distribution with p=1.5 and mean=1 is nonzero: data _null_; p=pdf('tweedie',0,1.5,1); put p=; run; ... View more

Yes, as stated in the note I referred to and in "Tweedie Distribution for Generalized Linear Models" in the Details section of the GENMOD documentation, the Tweedie distribution can be used for continuous response data with a mass of zero values. Unlike distributions with positive support like the gamma and log-normal, the Tweedie distribution supports zero values. I show a simple R-square-like statistic in the note for use as a goodness of fit measure and use it to compare the models presented there. The statistic is discussed further in the provided link. ... View more