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Annotated Stata Output: Ordered Logistic Regression [4/5/2016 8:05:36 PM] giving a gift Help the Stat Consulting Group by Stata Annotated Output Ordered Logistic Regression This page shows an example of an ordered logistic regression analysis with footnotes explaining the output. The data were collected on 200 high school students and are scores on various tests, including science, math, reading and social studies. The outcome measure in this analysis is socio-economic status ( ses )- low, medium and high- from which we are going to see what relationships exist with science test scores ( science ), social science test scores ( socst ) and gender ( female ). Our response variable, ses , is going to be treated as ordinal under the assumption that the levels of ses status have a natural ordering (low to high), but the distances between adjacent levels are unknown. The first half of this page interprets the coefficients in terms of ordered log-odds (logits) and the second half interprets the coefficients in terms of proportional odds. use , clear ologit ses science socst female Iteration 0: log likelihood = -210.58254 Iteration 1: log likelihood = -195.01878 Iteration 2: log likelihood = -194.80294 Iteration 3: log likelihood = -194.80235 Ordered logit estimates Number of obs = 200 LR chi2(3) = 31.56 Prob > chi2 = 0.0000 Log likelihood = -194.80235 Pseudo R2 = 0.0749 ------------------------------------------------------------------------------ ses | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- science | .0300201 .0165861 1.81 0.070 -.0024882 .0625283 socst | .0531819 .015271 3.48 0.000 .0232513 .0831126 female | -.4823977 .2796939 -1.72 0.085 -1.030588 .0657922 -------------+---------------------------------------------------------------- _cut1 | 2.754675 .869481 (Ancillary parameters) _cut2 | 5.10548 .9295388 ------------------------------------------------------------------------------ Iteration Log a Iteration 0: log likelihood = -210.58254 Iteration 1: log likelihood = -195.01878 Iteration 2: log likelihood = -194.80294 Iteration 3: log likelihood = -194.80235 a. This is a listing of the log likelihoods at each iteration. Remember that ordered logistic regression, like binary and multinomial logistic regression, uses maximum likelihood estimation, which is an iterative procedure. The first iteration (called iteration 0) is the log likelihood of the "null" or "empty" model; that is, a model with no predictors. At the next iteration, the predictor(s) are included in the model. At each iteration, the log likelihood increases because the goal is to maximize the log likelihood. When the difference between successive iterations is very small, the model is said to have "converged", the iterating stops, and the results are displayed. For more information on this process for binary outcomes, see Regression Models for Categorical and Limited Dependent Variables by J. Scott Long (pages 52-61). Model Summary Ordered logit estimates Number of obs c = 200 LR chi2(3) d = 31.56 Prob > chi2 e = 0.0000 Log likelihood = -194.80235 b Pseudo R2 f = 0.0749 b. Log Likelihood - This is the log likelihood of the fitted model. It is used in the Likelihood Ratio Chi-Square test of whether all predictors' regression coefficients in the model are simultaneously zero and in tests of nested models.

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