Title stata.com ologit — Ordered logistic regression

1 Ordered logistic regressionSyntaxMenuDescriptionOptionsRe marks and examplesStored resultsMethods and formulasReferencesAlso seeSyntaxologitdepvar[indepvars] [if] [in] [weight] [,options]optionsDescriptionModeloffset( varname)includevarnamein model with coefficient constrained to 1constraints(constraints)apply specified linear constraintscollinearkeep collinear variablesSE/Robustvce(vcetype)vcetypemay beoim,robust,clusterclustvar,bootstrap, orjackknifeReportinglevel(#)set confidence level; default islevel(95)orreport odds ratiosnocnsreportdo not display constraintsdisplayoptionscontrol column formats, row spacing, line width, display of omittedvariables and base and empty cells, and factor-variable labelingMaximizationmaximizeoptionscontr ol the maximization process; seldom usedcoeflegenddisplay legend instead of statisticsindepvarsmay contain factor variables; see[U] Factor contain time-series operators; see[U] Time-series ,by,fp,jackknife,mfp,mi estimate,nestreg,rolling,statsby,stepwis e, andsvyare allowed;see[U] Prefix (bootstrap)andvce(jackknife)are not allowed with themi estimateprefix; see [MI]mi are not allowed with thebootstrapprefix.

2 See [R] ()and weights are not allowed with thesvyprefix; see [SVY] ,iweights, andpweights are allowed; see[U] not appear in the dialog [U] 20 Estimation and postestimation commandsfor more capabilities of estimation >Ordinal outcomes> Ordered logistic regression12 ologit Ordered logistic regressionDescriptionologitfits Ordered logit models of ordinal variabledepvaron the independent actual values taken on by the dependent variable are irrelevant, except that larger values areassumed to correspond to higher [R]logisticfor a list of related estimation Model offset(varname),constraints(constraints) ,collinear; see [R]estimation options. SE/Robust vce(vcetype)specifies the type of standard error reported, which includes types that are derivedfrom asymptotic theory (oim), that are robust to some kinds of misspecification (robust), thatallow for intragroup correlation (clusterclustvar), and that use bootstrap or jackknife methods(bootstrap,jackknife); see [R]vceoption.

3 Reporting level(#); see [R]estimation the estimated coefficients transformed to odds ratios, that is,ebrather thanb. Standard errorsand confidence intervals are similarly transformed. This option affects how results are displayed,not how they are be specified at estimation or when replaying previouslyestimated ; see [R]estimation :noomitted,vsquish,noemptycells,baseleve ls,allbaselevels,nofvla-bel,fvwrap(#),fv wrapon(style),cformat(%fmt),pformat(%fmt ),sformat(%fmt), andnolstretch; see [R]estimation options. Maximization maximizeoptions:difficult,technique(algo rithmspec),iterate(#),[no]log,trace,grad ient,showstep,hessian,showtolerance,tole rance(#),ltolerance(#),nrtolerance(#),no nrtolerance, andfrom(initspecs); see [R]maximize.

4 These options areseldom following option is available withologitbut is not shown in the dialog box:coeflegend; see [R]estimation and logit models are used to estimate relationships between an ordinal dependent variable anda set of independent variables. Anordinalvariable is a variable that is categorical and Ordered , forinstance, poor , good , and excellent , which might indicate a person s current health status orthe repair record of a car. If there are only two outcomes, see [R] logistic , [R]logit, and [R] entry is concerned only with more than two outcomes. If the outcomes cannot be Ordered (forexample, residency in the north, east, south, or west), see [R]mlogit. This entry is concerned onlywith models in which the outcomes can be Ordered logistic regression 3In Ordered logit, an underlying score is estimated as a linear function of the independent variablesand a set of cutpoints.

5 The probability of observing outcomeicorresponds to the probability that theestimated linear function, plus random error, is within the range of the cutpoints estimated for theoutcome:Pr(outcomej=i) = Pr( i 1< 1x1j+ 2x2j+ + kxkj+uj i)ujis assumed to be logistically distributed in Ordered logit. In either case, we estimate the coefficients 1, 2,.., ktogether with the cutpoints 1, 2,.., k 1, wherekis the number of possibleoutcomes. 0is taken as , and kis taken as+ . All of this is a direct generalization of theordinary two-outcome logit 1We wish to analyze the 1977 repair records of 66 foreign and domestic cars. The data are avariation of the automobile dataset described in[U] Example datasets.

6 The 1977 repair records,like those in 1978, take on values Poor , Fair , Average , Good , and Excellent . Here is across-tabulation of the data:. use (Automobile Models). tabulate rep77 foreign, chi2 RepairRecordForeign1977 Domestic ForeignTotalPoor2 13 Fair10 111 Average20 727 Good13 720 Excellent0 55 Total45 2166 Pearson chi2(4) = Pr = it appears thatforeigntakes on the valuesDomesticandForeign, it is actually anumeric variable taking on the values 0 and 1. Similarly,rep77takes on the values 1, 2, 3, 4, and5, corresponding toPoor,Fair, and so on. The more meaningful words appear because we haveattached value labels to the data; see[U] Value the chi-squared value is significant, we could claim that there is a relationship betweenforeignandrep77.

7 Literally, however, we can only claim that the distributions are different; thechi-squared test is not directional. One way to model these data is to model the categorization thattook place when the data were created. Cars have a true frequency of repair, which we will assumeis given bySj= foreignj+uj, and a car is categorized as poor ifSj 0, as fair if 0< Sj 1, and so on:4 ologit Ordered logistic regression . ologit rep77 foreignIteration 0: log likelihood = 1: log likelihood = 2: log likelihood = 3: log likelihood = 4: log likelihood = logistic regression Number of obs = 66LR chi2(1) = > chi2 = likelihood = Pseudo R2 = Std.

8 Err. z P>|z| [95% Conf. Interval] .5308951 .4153425 .5988208 .3217706 .3136398 .3278925 .5423257 model isSj= +uj; the expected value for foreign cars is and, for domesticcars, 0; foreign cars have better repair estimated cutpoints tell us how to interpret the score. For a foreign car, the probability ofa poor record is the probability that +uj , or equivalently,uj Making thiscalculation requires familiarity with the logistic distribution: the probability is 1/(1+ ) = the other hand, for domestic cars, the probability of a poor record is the probabilityuj ,which is , it seems to us, is a far more reasonable prediction than we would have made based onthe table alone.

9 The table showed that 2 of 45 domestic cars had poor records, whereas 1 of 21foreign cars had poor records corresponding to probabilities 2/45= and 1/21= Thepredictions from our model imposed a smoothness assumption foreign cars should not, overall,have better repair records without the difference revealing itself in each category. In our data, thefractions of foreign and domestic cars in the poor category are virtually identical only because of therandomness associated with small if we were asked to predict the true fractions of foreign and domestic cars that would beclassified in the various categories, we would choose the numbers implied by the Ordered logit [R] ologit postestimationfor a more complete explanation of how to generate predictionsfrom an Ordered logit Ordered logistic regression 5 Technical noteHere Ordered logit provides an alternative to ordinary two-outcome logistic models with an arbitrarydichotomization, which might otherwise have been tempting.

10 We could, for instance, have summarizedthese data by converting the five-outcomerep77variable to a two-outcome variable, combining carsin the average, fair, and poor categories to make one outcome and combining cars in the good andexcellent categories to make the even less appealing alternative would have been to use ordinary regression , arbitrarilylabeling excellent as 5, good as 4, and so on. The problem is that with different but equally validlabelings (say, 10 for excellent ), we would obtain different estimates. We would have no way ofchoosing one metric over another. That assertion is not, however, true ofologit. The actual valuesused to label the categories make no difference other than through the order they fact, our labeling was 5 for excellent , 4 for good , and so on.