help for mscologit

mscologit - Multiscale ordered logit model

Syntax

mscologit depvars [if] [, indvar(indepvars) options]

Description

mscologit fits the multiscale ordered logit model that expresses the association between covariates indepvars and an ordinal outcome variable. mscologit is a generalization of the standard proportional odds ordered logit model,
but unlike the standard model, mscologit accommodates the presence of multiple response scales to measure the same rating dimension in the data, as when response formats for the same rating question differ across surveys or
survey waves. Alternative outcome variables are listed as depvars, but typically there is but one valid observation in depvars for each row of data (e.g., because each survey respondent had been presented with one particular response
format in a particular survey, country, survey wave, or sample split).

mscologit is a derivative of the proportional odds model, and is sharing all features of this ordered logit model. mscologit permits to relax the parallel lines assumption of the proportional odds model through its
lo and up options, whereby a multiscale variant of the generalized ordered logit model (Fu 1998, Williams 2006, 2016, Fullerton 2009, Agresti 2010, Fullerton and Xu 2016) may be estimated. As a wrapper for meglm,
gllamm, and runmlwin, mscologit also permits to implement multilevel specifications of the multiscale ordered logit model; in the current implementation, up to 5 hierarchical levels may be specified in mscologit.

Options

Standard (single-level) model specifications

depvars contains a variable list that corresponds to alternative measures of the outcome variable. Typically, there is only one valid observation on this variable list per row of data, because each respondent
(or unit of observation) had been confronted with one particular response format only. mscologit is estimating an ordered logit model on this data under the assumption that depvars constitute alternative ways of recording the
same latent dimension and that all depvars reflect ordinally ranked outcome data. Under this setting, mscologit estimates a common structural model Xb that applies to all observations irrespective of the concrete
response format of the particular depvar that a respondent i happened to answer. Like in the standard ordered logit model, mscologit produces estimates for the scale cutpoints aj, but mscologit does so
separately for each scale defined by one of the variables in depvars. Cutpoint estimates are labeled as /cS_J (with ML estimation) or cutp_S_J (when using mscologit as a wrapper) in the regression table,
where cutpoint S,J refers to S=1,..max-1 in the list of depvars (scales) and J to one of the categories j of scale S, with j numbered from J(S)=1,..max-1 and cutp_S_J referring to the conditional probability Pr(Y>j | S=s).
mscologit also handles the case where one or several dependent variables are being observed on a binary scale only.

indvar(indepvars) contains a variable list indepvars that corresponds to the independent variables. Factor variables and time-series notation is allowed, but avoiding either convenience notation may significantly speed up
mscologit with large datasets and many scales and response categories.

or requests mscologit to report coefficients as odds ratios rather than as regression coefficients on the logit scale. The coefficient format may also be changed through the replay function associated with the actual
(logit, meglm, gllamm, or runmlwin) estimation command.

logit is used to request estimating the multiscale model via logit regression on a suitably expanded dataset rather than via direct maximum likelihood estimation. In most situations, direct ML estimation will be the preferable option,
but the use of logit may be required when the number of model cutpoints becomes large (i.e. when being faced with a high number of rating scale formats and/or many long scales with a large number of response categories).

acc may be used to request the estimation of the model in its accelerating order parametrization, i.e. in the parametrization of cutpoint parameters as used in Stata's ologit estimation command.
acc will result in the same estimates for coefficients, but cutpoint parameters will become inverted relative to the standard output, as they now refer to the conditional probability Pr(Y<=j | S=s) rather than to Pr(Y>j | S=s).
acc is implicit when requesting full ML estimation of the single-level multiscale model, i.e. mscologit's ML estimator always implements the same model parametrization as does ologit.

vce(vcetype) may be used to request the computation of robust or clustered standard errors. Its specification follows standard Stata syntax, and all vcetypes supported by logit may also be used with mscologit.

lo may be used to relax the parallel regression assumption in the lower tail of the latent outcome variable. Use option lowcut(probability) to define the lower tail, and option lowvar(varlist)
to define the variables for which the parallel lines assumption is to be relaxed. When lowvar(varlist) is not specified, separate coefficients will be estimated for all indepvars.
The use of lo requires that all elements of depvar record outcomes by at least three response categories, the simultaneous use of lo and up requires that all elements of depvar record outcomes by at least
four response categories. Regression coefficients relating to the lower tail of the outcome distribution are labelled as lo_<varname> in the regression table.

up may be used to relax the parallel regression assumption in the upper tail of the latent outcome variable. Use option upcut(probability) to define the upper tail, and option upvar(varlist)
to define the variables for which the parallel lines assumption is to be relaxed. When upvar(varlist) is not specified, separate coefficients will be estimated for all indepvars.
The use of up requires that all elements of depvar record outcomes by at least three response categories, the simultaneous use of lo and up requires that all elements of depvar record outcomes by at least
four response categories. Regression coefficients relating to the upper tail of the outcome distribution are labelled as up_<varname> in the regression table.

altpar may be used to switch the format of regression coefficients in the generalized model specifications. The default behavior in mscologit is to estimate coefficients as interaction terms, which provides users
with a direct test of coefficient variability against the model for the middle part of the outcome distribution. altpar switches mscologit behavior to estimating separate regression coefficients
for each zone of the outcome distribution, and then corresponding hypothesis tests may be conducted using test and related post-estimation commands.

Additional options in multilevel model specifications

level2(levelspec), level3(levelspec), level4(levelspec), level5(levelspec) are being used to describe the regression specifications at higher levels of the data hierarchy.
The exact details of levelspec depend on the actual estimation command called by mscologit (i.e. meglm, gllamm, or runmlwin). Users should specify levelspec in exactly the same way as they would do
if using the original estimation command directly. mscologit is performing very limited syntax checking in itself, but will pass on levelspec to the actual estimation command mostly as specified by the user.
The specification of one or more levelX(levelspec) options requires the choice of either melogit, gllamm, or mlwin as the actual estimation command.

mlwin is used to call MLwiN for the estimation of the multilevel multiscale ordered logit model. This is the highly recommended option, given MLwiN's superior convergence behavior.
The use of MLwiN requires a copy of the software, which is available from the Centre for Multilevel Modelling at the University of Bristol (http://www.bristol.ac.uk/cmm/), and the runmlwin ado has to be installed
in order to call MLwiN from within Stata. The option mlwoptions(MLwiN_options) may be used to pass on any estimation option available in runmlwin, other than the levels specification provided by levelX(levelspec).
Also, when using mscologit with the mlwin option, it is the user's responsibility to declare the path for the MLwiN executable, see the runmlwin helpfile for details.

melogit is used to call Stata's internal meglm command for the estimation of the multilevel multiscale ordered logit model. The option melogoptions(melogit_options) may be used to pass on any estimation option
available in meglm, other than the levels specification provided by levelX(levelspec). By default, mscologit uses numerical derivatives and Stata's difficult option for ML estimation,
so model convergence may be somewhat slower than usual.

gllamm is used to call the gllamm ado command for the estimation of the multilevel multiscale ordered logit model. The use of gllamm requires that the gllamm ado has been installed before.
As with the other multilevel estimation commands, the option gllammoptions(gllamm_options) may be used to pass on any estimation option available in gllamm, other than the levels specification provided by levelX(levelspec).
By default, mscologit uses gllamm's adaptive quadrature routine as well as Stata's difficult option for ML estimation, so model convergence may therefore be slower than usual.

Examples

Single-level model

. mscologit depvar1 depvar2 depvar3, indvar(female educ age age2)

Single-level model, relaxing parallel regression assumption in the lower tail for all covariates, lower tail set to Pr(Y)<.33

. mscologit depvar1 depvar2 depvar3, indvar(female educ age age2) lo lowcut(.33)

Single-level model, relaxing parallel regression assumption in the lower tail for selected covariates, lower tail set to Pr(Y)<.33

. mscologit depvar1 depvar2 depvar3, indvar(female educ age age2) lo lowcut(.33) lowvar(female educ)

Multilevel model, using meglm/melogit

. mscologit depvar1 depvar2 depvar3, indvar(female educ age age2) melogit level2(levvar:)

Multilevel model, using MLwiN/runmlwin

. global MLwiN_path "C:\Program Files\MLwiN v3.05\mlwin.exe"

. gen cons = 1

. mscologit depvar1 depvar2 depvar3, indvar(female educ age age2) mlwin level2(levvar: cons) mlwopt(maxit(100) nopause)

Stored results

mscologit implements direct ML estimation of the basic specification of the multiscale ordered logit model, and acts as a wrapper for logit, meglm, gllamm, or runmlwin
when estimating multilevel or generalized specifications of the model. All stored results that are available after executing the original estimation commands, remain accessible after calling mscologit.
Likewise, the use of predict or margins is the same as when using the original estimation command that has been used in a run of the mscologit wrapper. To replay model estimates, use the original estimation command
(i.e. logit, meglm, gllamm, and runmlwin).

References

Agresti, Alan. 2010. Analysis of Ordinal Categorical Data. 2nd edition. Hoboken, NJ: Wiley.

Fu, Vincent Kang. 1998. "Sg88: Estimating Generalized Ordered Logit Models." Stata Technical Bulletin 8:160-64.

Fullerton, Andrew S. 2009. "A Conceptual Framework for Ordered Logistic Regression Models." Sociological Methods & Research 38(2):306-47. https://www.doi.org/10.1177/0049124109346162

Fullerton, Andrew S. and Jun Xu. 2016. Ordered Regression Models: Parallel, Partial, and Non-Parallel Alternatives. Boca Raton, FL: Chapman and Hall/CRC.

Williams, Richard. 2006. "Generalized Ordered Logit/Partial Proportional Odds Models for Ordinal Dependent Variables." Stata Journal 6(1):58-82. https://www.doi.org/10.1177/1536867X0600600104

Williams, Richard. 2016. "Understanding and Interpreting Generalized Ordered Logit Models." Journal of Mathematical Sociology 40(1):7-20. https://www.doi.org/10.1080/0022250X.2015.1112384

Author

Markus Gangl

School of Social Sciences (FB03)

Goethe University Frankfurt am Main

mailto:mgangl@soz.uni-frankfurt.de

mscologit is work in progress. The software comes without any warranties, but comments, bug reports, or any other
suggestions for improvement are welcome!

The development of mscologit has been made possible by the generous funding of the European Research Council (ERC)
under the European Commission's Horizon 2020 research and innovation programme (Grant Agreement no. 833196).
Neither the ERC nor the European Commission are responsible for this software or any of its uses.

Suggested citation

Markus Gangl (2023). A Generalized Ordered Logit Model to Accommodate Multiple Rating Scales. Sociological Methods & Research.
https://www.doi.org/10.1177/00491241231186655

Also see

logit, ologit, melogit, meglm, if installed: gologit, gologit2, gllamm, runmlwin