*! version 1.0.0 02mar2018
help probat

Title

probat -- calculates transition probabilities and other statistics after xtpdyn

Sintax

probat, stats[(atspec)] | prdistr
[margins(margins_options)] [nq(#)] [showfreq] [plot] [keep]

Description

probat is a postestimator command to be used after xtpdyn.
Either stats[(atspec)] or prdistr option must be specified.

If stats[(atspec)] is specified, probat computes ancillary statistics for the
overall sample or for the profile specified in atspec within stats(atspec).

If prdistr is specified, probat permits to capture the impact of
genuine state dependence at different levels of unobserved heterogeneity.

Note that probabilities are estimated using margins and many
margins options are allowed.

Options

Main

stats(atspec) defines the profile for which ancillary statistics are computed.
Ancillary statistics include entry Pr(1|0), exit Pr(0|1) and persistence Pr(1|1) probabilities,
the proportion of time spent in Y=1, the mean duration of the event and the turnover rate.
If only stats is specified, probat provides ancillary statistics
for the overal sample.
stats[(atspec)] may not be used with prdistr.

In option stats(atspec), atspec is defined as
varname1=# [varname2=# [...]]

prdistr computes predicted probabilities Pr(1|0) and Pr(1|1) at different
levels of unobserved heterogeneity (UH). It distinguishes UH in two components:
UHy attributable to the initial period of Y, and UHz attributable to the
initial period and the within-unit averages of time-varying explanatory variables.
Therefore, prdistr evaluates the probabilities Pr(1|0) and Pr(1|1) at all
the levels of the 2 UH components jointly. The first component is captured by the
levels of Yt0 (0/1). The second component is defined in terms of quantiles
of the UHz sample distribution computed on the basis of initial period
and the within-unit averages of time-varying explanatory variables.
prdistr may not be used with stats(atspec).

stats[(atspec)] Suboptions

margins(margins_options) specifies options usually allowed with margins.
See margins.

prdistr Suboptions

nq(#) specifies the number of quantiles used to split the distribution of
unobserved heterogeneity (UHz). nq() can assume only the following values: 2, 3, 4, 5, 10.
Default is nq(5).

showfreq shows frequancies for the outcome Y by Yt-1, Yt0 and UHz quantiles.

plot plots results of prdistr.

keep keeps the variables capturing the distribution of unobserved heterogeneity (UHz).

margins(margins_options) specifies options usually allowed with margins.
See margins.

Stored results

If stats[(atspec)] is specified probat stores the following in r():

Scalars

r(entry_pr) entry probability Pr(1|0)

r(exit_pr) exit probability Pr(0|1)

r(prop_t) proportion of time spent in y=1

r(meandur) mean duration

If either stats[(atspec)] or prdistr is specified probat stores the following in r():

Matrices

r(probest) matrix of predicted probabilities

Examples

Setup

. use poverty

Dynaminc random-effects probit model with unobserved heterogeneity

. xtpdyn poor black c.age i.edu i.emp i.marstat, uh(i.emp i.marstat age)

Ancillary statistics for the profile specified in stats(atspec)

. probat, stats(edu=1)

Ancillary statistics for the overall sample and confidence level at 90%

. probat, stats margins(level(90))

Predicted probabilites over unobserved heterogeneity, distinguishing UHz
in 4 quartiles and plotting the resutls

. probat, prdistr nq(4) plot

References

Boskin, M.J. and C.F. Nold 1975.
A Markov model of turnover in Aid for Families with Dependent Children.
Journal of Human Resources 10: 467-481.

Cappellari, L. and S.P. Jankins 2009.
The dynamic of social assistance benefit receipt in Britain.
ISER Working Paper Series: 2009-2029.

Immervoll, H., Jenkins S., and Königs, S. 2015.
Are Recipients of Social Assistance ‘Benefit Dependent’?: Concepts,
Measurement and Results for Selected Countries
OECD Social, Employment and Migration Working Papers, No. 162, OECD Publishing, Paris.

Authors

Raffaele Grotti <raffaele.grotti@esri.ie>

The Economic and Social Research Institute

Whitaker Square

Sir John Rogerson's Quay, Dublin 2

Ireland

Giorgio Cutuli <g.cutuli@unitn.it>

Department of Sociology and Social Research

University of Trento

Via Verdi, 26-I-38122 Trento

Italy

Also see

xtpdyn margins

For further details on model implementation and a more detailed example see:

Grotti, R. and G. Cutuli 2018.
Estimating dynamic random effects probit model with unobserved heterogeneity using Stata