Multinomial Ordinal Regression Custom Hypothesis Testing for Middle Group in Dependent Variable

[ROLuke91]

Hi all,

I am attempting to perform a multinomial logistic regression to predict a 3-level ordinal DV (Y = {0,1,2}) with a 3-level nominal IV (Y = {2,3,4}, but non-ordered). I would like to produce the following output: 

Odds of "Yes vs. No" in being in category 2 in DV, when in category 2 in IV

Odds of "Yes vs. No" in being in category 2 in DV, when in category 3 in IV

Odds of "Yes vs. No" in being in category 2 in DV, when in category 4 in IV

Ditto for above, but for category 1 in DV

Ditto for above, but for category 0 in DV

Using PROC Surveylogistic, I have the following two blocks of code:

Block 1:

proc surveylogistic data=A
weight weight;
class X (ref = '4') / param = ref;
model Y(descending) = X;
estimate 'Odds of Y = 1 OR 2 due to X = 2' intercept 1 X 2 / CL EXP Category = '1';
estimate 'Odds of Y = 2 due to X = 2' intercept 1 X 2 / CL EXP Category = '2';

estimate 'Odds of Y = 1 OR 2 due to X = 3' intercept 1 X 3 / CL EXP Category = '1';

estimate 'Odds of Y = 2 due to X = 3' intercept 1 X 3 / CL EXP Category = '2';

estimate 'Odds of Y = 1 OR 2 due to X = 4' intercept 1 X 4 / CL EXP Category = '1';

estimate 'Odds of Y = 2 due to X = 4' intercept 1 X 4 / CL EXP Category = '2';

run;

Block 2:

proc surveylogistic data=A
weight weight;
class X (ref = '4') / param = ref;
model Y= X;
estimate 'Odds of Y = 0 due to X = 2' intercept 1 X 2 / CL EXP Category = '0';
estimate 'Odds of Y = 0 due to X = 3' intercept 1 X 2 / CL EXP Category = '0';

estimate 'Odds of Y = 0 due to X = 4' intercept 1 X 3 / CL EXP Category = '0';

run;

To my understanding, the above two procs give me the following:

1. Odds of "Yes vs. No" in being in category 2 in DV, when in category {2,3,4} in IV <- Block 1

2. Odds of "Yes vs. No" in being in AT LEAST category 2 in DV (category 1 OR 2), when in category {2,3,4} in IV <- Block 1

3. Odds of "Yes vs. No" in being in category 0 in DV, when in category {2,3,4} in IV <- Block 2

Question: How can I use Estimate statements to extract "Odds of 'Yes vs. No' in being in category 1 in DV when in category {2,3,4} in IV?" I am confused about how to obtain Odds Ratios for the middle category, given my understanding on how ordinal logistic regression custom hypothesis testing works using PROC Surveylogistic Estimate statements.

[StatDave]

The odds of Y=2 given X=2 means Pr(Y=2)/Pr(Y=1 or 3) when X=2. I suspect this is not really what you want. I'm guessing what you want is an estimate of Pr(Y=2) given X=2 and similarly for the probabilities of the other Y levels at each X level. You could get that easily by using the PREDPROBS=INDIVIDUAL option in the OUTPUT statement. It provides the estimated probability of each response level for each observation. ESTIMATE statements with EXP will give you cumulative odds (such as Pr(Y=0)/Pr(Y=1 or 2) and Pr(Y=0 or 1)/Pr(Y=2)). In any case, the coefficients that you have following X in the ESTIMATE statements should be a list like 1 0 to select level 2 of X since X is categorical and has two estimated parameters. Add the E option so see the coefficients that are used to multiply the model parameters.