lec7 - VII. Ordinal & Multinomial Logit Models To what...

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Unformatted text preview: VII. Ordinal & Multinomial Logit Models To what degree do the dietary & exercise habits of a sample of adults predict whether they are in the low, medium, or high-risk categories for cardiovascular disease? How well do the social traits of a sample of high school students predict whether their achievement test scores are low, medium-low, medium-high, or high? To what extent do the institutional characteristics of a sample of political regimes predict whether their responsiveness to citizen demands is low, medium, or high? How helpful are the institutional characteristics of a sample of industrial firms in predicting whether the amount of pollution they emit is low, medium, or high? These are examples of ordinal outcome variables. The categories of an ordinal variable can be ranked, but the distances between the categories are not equal. Because the distances between the categories are not equal, analyzing ordinal outcome variables via OLS regression violates its assumptions & leads to erroneous conclusions. What statistical model avoids the assumption of equal intervals between ordinal categories? Logit & probit versions of the ordinal regression model safely ignore the OLS assumption of equal intervals between a variable’s categories. But as Long & Freese (pages 137-38) observe, “Simply because the values of a variable can be ordered does not imply that the variable should be analyzed as ordinal.” A categorical, multi-level variable could conceivably be ordered for one purpose but unordered for another. As Long & Freese conclude, “Overall, when the proper ordering is ambiguous, the models for nominal outcomes [ multinomial regression ] …should be considered.” Multinomial models treat categories as nominal rather than ordinal: Which do you prefer—apple pie, hot fudge sundae, cheese cake, or cannoli? Which is your racial-ethnic identity: Black, White, Asian, Hispanic, or other? Let’s use ordinal logistic regression to analyze respondent answers to this statement: “A working mother can establish just as warm & secure of a relationship with her child as a mother who does not work.” The responses are coded as: 1=strongly disagree (SD), 2=disagree (D), 3=agree (A), & 4=strongly agree (SA). These data are examined in Long/Freese, chapter 5. . use ordwarm2, clear Let’s assume we’ve done the preparatory data analysis & transformations. . ologit warm yr89 male white age ed prst, or nolog table . ologit warm yr89 male white age ed prst, or nolog table Ordered logit estimates Number of obs = 2293 LR chi2(6) = 301.72 Prob > chi2 = 0.0000 Log likelihood = -2844.9123 Pseudo R2 = 0.0504------------------------------------------------------------------------- warm | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------------------------------------------------- yr89 | 1.688605 .1349175 ....
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This note was uploaded on 07/11/2011 for the course SYA 6306 taught by Professor Tardanico during the Spring '09 term at FIU.

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lec7 - VII. Ordinal & Multinomial Logit Models To what...

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