See this note which describes models you could consider for a continuous response that is zero inflated.  ... View more

See the NLMeans documentation. The Details section mentions the Hessian warning and that it can be ignored. Your GENMOD results probably seem backward because you didn't include the EVENT="1" response variable options like you did in LOGISTIC. Also, your model in GENMOD is a log-binomial model and it is prone to fitting errors as described in Note 23003 which suggests possible solutions. Finally, the Poisson model, also discussed in Note 23003, is another method indeed intended for a binary response, not a count response. In the example shown, notice that the OUTCOME variable is binary. That model is probably a better one to use than the log-binomial model because of the fitting problems that the latter can have. ... View more

You could use the SPEC option in the MODEL statement in PROC REG. That and related options are discussed in "Testing for Heteroscedasticity" in the Details section of the REG documentation in the SAS/STAT User's Guide. ... View more

That suggests that one or more of your predictors does not have a constant parameter across the various logits. You can fit a nonproportional odds model using the EQUALSLOPES and UNEQUALSLOPES options as discussed and illustrated in this note. Also see the example titled "Partial Proportional Odds Model" in the LOGISTIC documentation. ... View more

I assume you are asking about the output produced by the LSMEANS statement. In the first table, the Estimate column provides estimates of the log odds for higher levels of the response, assuming that the DESCENDING response variable option is used as I showed. The Mean column provides estimates of the cumulative probabilities, Pr(X<=x). The Differences table provides the difference (as indicated in the first two columns) in log odds between each pair of treatments or products. The Estimate column is the estimated difference in log odds - equivalently the log odds ratio - for each pair. If you want the estimated odds ratios, add the ODDSRATIO option in the LSMEANS statement.   Note that these PROC LOGISTIC statements model a set of 4 cumulative logits defined on your 5-level response and assumes that the parameters for all predictor variables are the same across those logits, differing only on their intercepts. This is the so-called proportional odds assumption. A test of that assumption is included in the PROC LOGISTIC output. As a result of this assumption, the odds ratio between two treatments is the same regardless of which response level considered. If the assumption is violated (as indicated by a small p-value from the assumption test), then a more complex model and analysis is needed. ... View more

No, the ESTIMATE statement cannot be used. As I noted and as you can see in the expressions in each line of the FDATA= data set, the odds ratio estimate for increasing X by u units is computed by evaluating the model at x+u and at x and then differencing the results and finally exponentiating the difference. Each evaluation is a log odds, so their difference is a log odds ratio. Exponentiating then gives the odds ratio estimate. This computation is a nonlinear function of the model parameters. The ESTIMATE statement can only compute linear functions of the model parameters.   I believe what you suggest with the ESTIMATE statement actually estimates the odds ratio for multiplying X by 5 or 10, not for adding 5 or 10 units:   logit(5x)=a+b(log(5x)=a+b(log(x)+log(5)) -logit(x)=                         a+b(log(x)) = b*log(5) ... View more

If you want to do this as part of an analysis of observed data and obtain estimates of the odds ratio at various values of X (since the odds ratio changes with X) along with tests that the odds ratio equals 1 and confidence intervals, you can use the NLEST macro. That macro is needed since, as has been shown, the odds ratio on X is a nonlinear function of the model parameters. Following is an example with random data from known model logit(p)=a+bX with a and b values as specified. The model on log(x) is estimated and saved with PROC LOGISTIC and then the NLEST macro is used to evaluate the model at log(x+1) and log(x), for various x, and exponentiating their difference. As noted, the evaluating expressions in the FDATA= data set could be simplified to [(x+1)/x]**b. Change the "+1" in the expressions to another value if you want to evaluate an increase of other than 1 unit. Alternatively, you could use the macro to estimate the increase in risk (event probability) using data lines like at x=1 , logistic(b_p1+log(1+1)*b_p2) - logistic(b_p1+log(1)*b_p2) or even to evaluate the risk ratio for increasing X with data lines like at x=1 , logistic(b_p1+log(1+1)*b_p2) / logistic(b_p1+log(1)*b_p2) data a; n=10000; a=-2.5; b=2; do lnx=0 to 1 by .1; x=exp(lnx); logit=a+b*lnx; truodds=exp(logit); truodxp1=exp(a+b*log(x+1)); truor=truodxp1/truodds; p=logistic(logit); y=rand("binomial",p,n); output; end; run; proc logistic data=a; model y/n = lnx; effectplot / link; store log; run; data fd; length label f $32767; infile datalines delimiter=','; input label f; datalines; at x=1 , exp( (b_p1+log(1+1)*b_p2) - (b_p1+log(1)*b_p2) ) at x=1.5 , exp( (b_p1+log(1.5+1)*b_p2) - (b_p1+log(1.5)*b_p2) ) at x=2 , exp( (b_p1+log(2+1)*b_p2) - (b_p1+log(2)*b_p2) ) at x=2.5 , exp( (b_p1+log(2.5+1)*b_p2) - (b_p1+log(2.5)*b_p2) ) ; %nlest(instore=log, fdata=fd, null=1, title=ORs at various X values) ... View more

Note that when you use the ESTIMATE statement in PROC GENMOD, the results automatically include a "Mean Estimate" which, in your case, is 1.51. But this is a mean only when the contrast specified in the statement defines one population and not a comparison of populations such as a difference in difference contrast. The Mean estimate just applies the inverse of the link function to the computed contrast and is often meaningless. For the difference in difference contrast (1 -1 -1 1) in a log linked model, the Mean estimate is exp[log(mean_11)-log(mean_10)-log(mean_01)+log(mean_00)] which, when simplified is the ratio of mean ratios rather than the difference of mean differences: (mean_11/mean_10)/(mean_01/mean_00). ... View more

Reread the text at the beginning of the "Generalized Linear Models with a Non-Identity Link" section - this section, and not the first section on a normal response, applies to your log-linked model. As stated there: "Because this is not a linear combination of the model parameters or of the LS-means, you cannot use the ESTIMATE or LSMESTIMATE statements to estimate the difference in differences of means. " ... View more