Stata 15 help for rologit

[R] rologit -- Rank-ordered logistic regression

Syntax

rologit depvar indepvars [if] [in] [weight], group(varname) [options]

options Description ------------------------------------------------------------------------- Model * group(varname) identifier variable that links the alternatives offset(varname) include varname in model with coefficient constrained to 1 incomplete(#) use # to code unranked alternatives; default is incomplete(0) reverse reverse the preference order notestrhs keep right-hand-side variables that do not vary within group ties(spec) method to handle ties: exactm, breslow, efron, or none

SE/Robust vce(vcetype) vcetype may be oim, robust, cluster clustvar, bootstrap, or jackknife

Reporting level(#) set confidence level; default is level(95) display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Maximization maximize_options control the maximization process; seldom used

coeflegend display legend instead of statistics ------------------------------------------------------------------------- *group(varname) is required. indepvars may contain factor variables; see fvvarlist. bootstrap, by, fp, jackknife, rolling, and statsby are allowed; see prefix. Weights are not allowed with the bootstrap prefix. fweights, iweights, and pweights are allowed, except with ties(efron); see weight. coeflegend does not appear in the dialog box. See [R] rologit postestimation for features available after estimation.

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Statistics > Ordinal outcomes > Rank-ordered logistic regression

Description

rologit fits the rank-ordered logistic regression model by maximum likelihood (Beggs, Cardell, and Hausman 1981). This model is also known as the Plackett-Luce model (Marden 1995), as the exploded logit model (Punj and Staelin 1978), and as the choice-based method of conjoint analysis (Hair et al. 2010).

rologit expects the data to be in long form, similar to clogit, in which each of the ranked alternatives forms an observation; all observations related to an individual are linked together by the variable that you specify in the group() option. The distinction from clogit is that depvar in rologit records the rankings of the alternatives, whereas for clogit, depvar marks only the best alternative by a value not equal to zero. rologit interprets equal scores of depvar as ties. The ranking information may be incomplete "at the bottom" (least preferred alternatives). That is, unranked alternatives may be coded as 0 or as a common value that may be specified with the incomplete() option.

If your data record only the unique alternative, rologit fits the same model as clogit.

Options

+-------+ ----+ Model +------------------------------------------------------------

group(varname) is required, and it specifies the identifier variable (numeric or string) that links the alternatives for an individual, which have been compared and rank ordered with respect to one another.

offset(varname); see [R] estimation options.

incomplete(#) specifies the numeric value used to code alternatives that are not ranked. It is assumed that unranked alternatives are less preferred than the ranked alternatives (that is, the data record the ranking of the most preferred alternatives). It is not assumed that subjects are indifferent between the unranked alternatives. # defaults to 0.

reverse specifies that in the preference order, a higher number means a less attractive alternative. The default is that higher values indicate more attractive alternatives. The rank-ordered logit model is not symmetric in the sense that reversing the ordering simply leads to a change in the signs of the coefficients.

notestrhs suppresses the test that the independent variables vary within (at least some of) the groups. Effects of variables that are always constant are not identified. For instance, a rater's gender cannot directly affect his or her rankings; it could affect the rankings only via an interaction with a variable that does vary over alternatives.

ties(spec) specifies the method for handling ties (indifference between alternatives) (see [ST] stcox for details):

exactm exact marginal likelihood (default) breslow Breslow's method (default if pweights specified) efron Efron's method (default if robust VCE) none no ties allowed

+-----------+ ----+ SE/Robust +--------------------------------------------------------

vce(vcetype) specifies the type of standard error reported, which includes types that are derived from asymptotic theory (oim), that are robust to some kinds of misspecification (robust), that allow for intragroup correlation (cluster clustvar), and that use bootstrap or jackknife methods (bootstrap, jackknife); see [R] vce_option.

If ties(exactm) is specified, vcetype may be only oim, bootstrap, or jackknife.

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Maximization +-----------------------------------------------------

maximize_options: iterate(#), trace, [no]log, tolerance(#), ltolerance(#), nrtolerance(#), and nonrtolerance; see [R] maximize. These options are seldom used.

The following option is available with rologit but is not shown in the dialog box:

coeflegend; see [R] estimation options.

Examples

You have data in which subjects ranked up to four options. rologit requires that the data be in "long format", in which the responses of one subject are recorded in different records (observations).

caseid depvar option x1 x2 male 1 4 1 1 0 0 1 2 2 0 1 0 1 3 3 0 0 0 1 1 4 1 1 0

2 1 1 3 0 0 2 3 2 0 1 0 2 3 3 2 1 0 2 4 4 1 2 0

3 1 1 3 1 1 3 3 2 1 1 1 3 4 4 0 1 1

4 2 1 1 1 1 4 1 2 1 1 1 4 0 3 0 1 1 4 0 4 1 0 1

where 0 indicates that subject 4 only specified his two most favorable alternatives. In this example

subject 1 has ranking

option_1 > option_3 > option_2 > option_4

subject 2 has a ranking with ties,

option_4 > option_2 == option_3 > option_1

subject 3 ranked a subset of alternatives, ignoring option 3,

option_4 > option_2 > option_1

subject 4 had an incomplete ranking

option_1 > option_2 > (option_3,option_4)

Subject 4 ranked option_1 highest among all four options, and ranked option_2 highest among the remaining three options. His preference ordering among option_3 and option_4, however, is not known.

. webuse rologitxmpl2

You can fit a rank-ordered logit model for the four alternatives as

. rologit depvar x1 x2, group(caseid)

More complicated models may be formulated as well. We can perform a likelihood-ratio test that men and women rank the options in the same way (note that the main effect of gender is not identified),

. estimates store base . rologit depvar x1 x2 male#c.x1 male#c.x2, group(caseid) . estimates store full . lrtest base full

A note on data organization

Sometimes your data will be in a "wide format" in which the ranking of options are described in a series of variables, rather than in different observations that are associated with one subject.

caseid opt1 opt2 opt3 opt4 1 4 2 3 1 2 1 3 3 4 3 1 3 . 4 4 2 1 0 0

You may want to verify that this information is identical to the data in long format listed above. The Stata command reshape makes the transformation between "long" and "wide" formats quite simple,

. reshape long opt, i(caseid) j(option) . drop if missing(opt)

Stored results

rologit stores the following in e():

Scalars e(N) number of observations e(ll_0) log likelihood of the null model ("all rankings are equiprobable") e(ll) log likelihood e(df_m) model degrees of freedom e(chi2) chi-squared e(p) p-value for model test e(r2_p) pseudo-R^2 e(N_g) number of groups e(g_min) minimum group size e(g_avg) average group size e(g_max) maximum group size e(code_inc) value for incomplete preferences e(N_clust) number of clusters e(rank) rank of e(V) e(converged) 1 if converged, 0 otherwise

Macros e(cmd) rologit e(cmdline) command as typed e(depvar) name of dependent variable e(group) name of group() variable e(wtype) weight type e(wexp) weight expression e(title) title in estimation output e(clustvar) name of cluster variable e(offset) linear offset variable e(chi2type) Wald or LR; type of model chi-squared test e(reverse) reverse, if specified e(ties) breslow, efron, exactm e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(properties) b V e(predict) program used to implement predict e(marginsok) predictions allowed by margins e(marginsnotok) predictions disallowed by margins e(marginsdefault) default predict() specification for margins e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(V) variance-covariance matrix of the estimators e(V_modelbased) model-based variance

Functions e(sample) marks estimation sample

References

Beggs, S., S. Cardell, and J. A. Hausman. 1981. Assessing the potential demand for electric cars. Journal of Econometrics 17: 1-19.

Hair, J. F., Jr., W. C. Black, and B. J. Babin, and R. E. Anderson. 2010. Multivariate Data Analysis. 7th ed. Upper Saddle River, NJ: Pearson.

Marden, J. I. 1995. Analyzing and Modeling Rank Data. London: Chapman & Hall.

Punj, G. N., and R. Staelin. 1978. The choice process for graduate business schools. Journal of Marketing Research 15: 588-598.


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