Chp 7 Logit Models for Multivariate Responses

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Presentation transcript:

Chp 7 Logit Models for Multivariate Responses 7.1: Model for Nominal Response; 7.2: Model for Ordinal Response; 7.3: other link functions; 7.4: alternative ordinal-response models; 7.5: test of conditional independence; 7.6: discrete-choice multinomial logit models.

7.1 Nominal Responses: Baseline-Category Logit Model

7.1.2 Alligator Food Choice Example

Variables:

SAS code: data gator; input lake gender size food count @@; datalines; 1 1 1 1 7 … 4 2 2 5 1 proc logistic; freq count; class lake size / param=ref; model food(ref='1') = lake size / link=glogit aggregate scale=none; proc catmod; weight count; population lake size gender; model food = lake size / pred=freq pred=prob; run; population lake size;

Results Absolute values of standard Pearson residuals comparing the observed and fitted values exceed 2 in only two of the 40 cells and exceed 3 in none of the cells. So, this fit seems adequate. With fish as the baseline category, Table 7.4 contains ML estimates of effect parameters. The model uses dummy variables for first three lakes and for size.

7.2 Ordinal Responses: Cumulative Logit Models

SAS code data impair; input mental ses life; datalines; 1 1 1 … 4 0 9 ; proc genmod ; model mental = life ses / dist=multinomial link=clogit lrci type3; Run;