NASUG2005 - gologit2 Generalized Logistic Regression Partial Proportional Odds Models for Ordinal Dependent Variables Richard Williams Department of

NASUG2005 - gologit2 Generalized Logistic Regression...

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gologit2: Generalized Logistic Regression/ Partial Proportional Odds Models for Ordinal Dependent Variables Richard Williams Department of Sociology University of Notre Dame July 2005

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Key features of gologit2 Backwards compatible with Vincent Fu’s original gologit program – but offers many more features Can estimate models that are less restrictive than ologit (whose assumptions are often violated) Can estimate models that are more parsimonious than non-ordinal alternatives, such as mlogit
Specifically, gologit2 can estimate: Proportional odds models (same as ologit – all variables meet the proportional odds/ parallel lines assumption) Generalized ordered logit models (same as the original gologit – no variables need to meet the parallel lines assumption) Partial Proportional Odds Models (some but not all variables meet the pl assumption)

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Example 1: Proportional Odds Assumption Violated (Adapted from Long & Freese, 2003 – Data from the 1977 & 1989 General Social Survey) Respondents are asked to evaluate the following statement: “A working mother can establish just as warm and secure a relationship with her child as a mother who does not work.” 1 = Strongly Disagree (SD) 2 = Disagree (D) 3 = Agree (A) 4 = Strongly Agree (SA).
Explanatory variables are yr89 (survey year; 0 = 1977, 1 = 1989) male (0 = female, 1 = male) white (0 = nonwhite, 1 = white) age (measured in years) ed (years of education) prst (occupational prestige scale).

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Ologit results . ologit warm yr89 male white age ed prst 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 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- yr89 | .5239025 .0798988 6.56 0.000 .3673037 .6805013 male | -.7332997 .0784827 -9.34 0.000 -.8871229 -.5794766 white | -.3911595 .1183808 -3.30 0.001 -.6231815 -.1591374 age | -.0216655 .0024683 -8.78 0.000 -.0265032 -.0168278 ed | .0671728 .015975 4.20 0.000 .0358624 .0984831 prst | .0060727 .0032929 1.84 0.065 -.0003813 .0125267 -------------+---------------------------------------------------------------- _cut1 | -2.465362 .2389126 (Ancillary parameters) _cut2 | -.630904 .2333155 _cut3 | 1.261854 .2340179 ------------------------------------------------------------------------------
Interpretation of ologit results These results are relatively straightforward, intuitive and easy to interpret. People tended to be more supportive of working mothers in 1989 than in 1977. Males, whites and older people tended to be less supportive of working mothers, while better educated people and people with higher occupational prestige were more supportive. But, while the results may be straightforward, intuitive, and easy to interpret, are they correct? Are the assumptions of the ologit model met? The following Brant test suggests they are not.

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Brant test shows assumptions violated . brant Brant Test of Parallel Regression Assumption Variable | chi2 p>chi2 df -------------+-------------------------- All | 49.18 0.000 12 -------------+-------------------------- yr89 | 13.01 0.001 2 male | 22.24 0.000 2 white | 1.27 0.531 2 age | 7.38 0.025 2 ed | 4.31 0.116 2 prst | 4.33 0.115 2 ---------------------------------------- A significant test statistic provides evidence that the parallel regression assumption has been violated.
How are the assumptions violated? . brant, detail Estimated coefficients from j-1 binary regressions y>1 y>2 y>3 yr89 .9647422 .56540626 .31907316 male -.30536425 -.69054232 -1.0837888 white -.55265759 -.31427081 -.39299842 age -.0164704 -.02533448 -.01859051 ed .10479624 .05285265 .05755466 prst -.00141118 .00953216 .00553043 _cons 1.8584045 .73032873 -1.0245168 This is a series of binary logistic regressions. First it is 1 versus 2,3,4; then 1 & 2 versus 3 & 4; then 1, 2, 3 versus 4

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