Date: Fri, 6 Jan 2006 12:59:45 -0800 Kevin "SAS(r) Discussion" Kevin http://groups.google.com Interpreting Proc Logistic- Odds ratios to probability To: sas-l@uga.edu text/plain; charset="iso-8859-1"

Hello all and Happy New Year, I am running analyses on the presence of fish associated with an artificial reef and have a few questions regarding the interpretation of the output.

My response variable is binary (FishPres= 0 or 1) with 4 explanatory variables : Season= 1, 2 (First 6 months or last 6 months of year) Depth_Bin = 1, 2, 3 (Depth intervals) Area_Infl = 1,2 (Area of influence of reef) Quad= 1, 2, 3, 4 (Quadrant of reef)

Proc Logistic data=two descending order=data; Class season depth_bin area_infl quad /param=glm; Model fishpres (event='1')= season vert area_infl quad /expb; Contrast 'Depth-Up vs. Mid&Low' vert -2 1 1 / estimate=exp; Contrast 'Reef Area- (1-3 vs 4)' quad -1 -1 -1 3 /estimate=exp; Contrast 'Reef Clusters- (1&3 vs 2&4)' quad 1 -1 1 -1 /estimate=exp; Output out=next1 predicted=yhat lower=lcl upper=ucl; run; Odds Ratio Estimates Point 95% Wald Effect Estimate Confidence Limits Season 1 vs 2 2.440 2.365 2.517 Depth_bin 1 vs 3 0.429 0.414 0.445 Depth_bin 2 vs 3 0.515 0.498 0.532 Area_infl 1 vs 2 2.329 2.255 2.405 Quad 1 vs 4 1.093 1.045 1.144 Quad 2 vs 4 1.479 1.420 1.540 Quad 3 vs 4 1.213 1.162 1.267

Contrast Rows Estimation and Testing Results Contrast Type Row Est. ChiSq Depth- Mid vs Lower(2 vs3) EXP 1 0.5150 <.0001 Quad- Reef habitats(1-3 vs 4) EXP 1 0.5098 <.0001 Quad- Reef Cluster(1&3 vs 2&4) EXP 1 0.8970 <.0003

I am trying to describe the distribution of fish associated with the reef and am interested in the probability of detection given season, and position on reef (depth, quad, etc.). given that these variables are all categorical the output provides estimates and odd ratio estimates for each level compared to the last (reference) level.

1. Given the above model, how do I construct probability estimates of detecting a fish given depth or area_infl? Furthermore, could I derive an estimate of the increase or decrease in probability with changes in depth or position on reef using the odds ratio estimates provided in the above output.

2. Must I incorporate an interaction term if I want to discuss fish presence across depth intervals or reef attributes by season? The reason I ask is becasue it takes approx 30 min to run the models with the interaction term. Additionally, if I do include an interaction term, how do I construct a contrast statment for the interaction effect?

3. Can contrast estimates be interpreted as odds ratios? Some of the contrasts I have constructed previously have (as I understand it) replicated tests of the main effects, thereby producing the save values as the odds ratios.

Many thanks and kind regards,

Kevin Boswell

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