MODELING SELECTION WITH MULTINOMIAL
TREATMENT MODELS: AN EXAMPLE USING
PARENTAL ROLES
KEVIN SHAFER
SCHOOL OF SOCIAL WORK
BRIGHAM YOUNG UNIVERSITY
HOUSEKEEPING
 Garrett Pace, Center for Research on Child Wellbeing at Princeton
University, is a co-author on this project
 We have a paper in press at Health & Social Work that uses this method.
We are happy to share.
 You can also email me for Stata code, etc. on these models.
 A very helpful article is Deb & Trivedi (2006) in Stata Journal.
SUBSTANTIVE BACKGROUND
 1 in 6 adults experience a major depressive episode in their lifetimes
 Women are 2-3 times more likely to get a depression diagnosis (although
there are issues with measurement, etc.)
 Parenting may be a risk factor for depressive symptoms
 Parenting quality is associated with depressive symptoms.
 Parents are less likely to be screened for MDD and treatment is less
common for moms and dads
SUBSTANTIVE BACKGROUND
 Most studies of parenting and depression link depressive symptoms to
stress
 Does parenting stress vary by the kind of parental role(s) one has?
 Parental roles are, in part, defined by one’s gender, marital status, etc.
 Prior research is inconclusive on the link between parenting and depression
 Methodological issues?
 Selection effects?
WHY SELECTION MATTERS…
 Social scientists worry (a lot) about selection
 Some examples:
 Cohabitation and likelihood of divorce
 Divorce and subjective well-being
 Lower marital quality in remarriage
 Many, many more
 Recently, models such as propensity score modeling have been developed
to account for selection
A BASIC DESCRIPTION OF PSM
Treated
Not Treated
Person n’s
subjective wellbeing
SWB
SWB
Selection: unhappily married
people tend to divorce, happily
married people tend not to.
Does this happiness level
influence post-divorce SWB?
SWB
SWB
SWB
Treatment= divorce. We
match individuals on
divorce proneness (typically
within 0.25 SD of each
other on the measure).
Thus, we try to isolate the
effect of divorce on
subjective well-being via
this comparison.
MULTINOMIAL TREATMENT MODELS
Married
Various personal
characteristics, such as:
age, race/ethnicity,
educational attainment,
other measures of SES,
family-of-origin
measures, attitudes
about family and
gender, etc. and
unmeasured variables
Never Married
Cohabiting
Divorced
Remarried
METHODOLOGICAL ISSUES
 Data come from NLSY79 (restricted sample= 6,276)
 Baseline CES-D 7 depression score: 1992 or 1994 (age 27-37 at baseline).
There are no significant difference in T1 depression score by year or initial
age.
 T2 depression score measured in Age 40 or 50 Health Evaluations (most in
2000-2006 waves)
MULTINOMIAL TREATMENT MODEL
 Selection on the key independent variable
 Two stage model:
1)
Selection is modeled via a set of variables associated with entry into the
independent variable
2)
Model dependent variable on independent and control variables, with a
correction for selection (as noted by Λ )
 Models are run in Stata 13 using the user-written command mtreatreg
MULTINOMIAL TREATMENT MODEL
 Our example will use a variable for number of parental roles
 0: no parental roles (33%)
 1: one parental role (36%)
 2: two parental roles (25%)
 3: 3 or more parental roles (6%)
STATA CODE
findit mtreatreg //to download command
mtreatreg d_t2 female nmar pmar cohabit rm d_t1
emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year,mtreat(nroles= female nmar pmar cohabit
rm d_t1 emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year) sim(100) dens(normal) difficult
STATA CODE
findit mtreatreg //to download command
mtreatreg d_t2 female nmar pmar cohabit rm d_t1
emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year, mtreat(nroles= female nmar pmar cohabit
rm d_t1 emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year) sim(100) dens(normal) difficult
STATA CODE
findit mtreatreg //to download command
mtreatreg d_t2 female nmar pmar cohabit rm d_t1
emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year,mtreat(nroles= female nmar pmar cohabit
rm d_t1 emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year) sim(200) dens(normal) difficult
STATA CODE
findit mtreatreg //to download command
mtreatreg d_t2 female nmar pmar cohabit rm d_t1
emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year,mtreat(nroles= female nmar pmar cohabit
rm d_t1 emply linc lhs hsg sc south urban black
hispanic catholic cp orel norelig relfreq
t2year) sim(200) dens(normal) difficult
Logged Relative Risk of Number of Parental Roles from Stage 1 of MTM
No roles vs. One Two roles vs. One Three or more
role
role
roles vs. One role
Female
-0.925***
0.070
-0.189
Never married
3.435***
-0.302
-0.118
Previously married
1.903***
-0.038
0.294
Cohabiting
1.886***
-0.027
-0.105
Remarried
0.755***
0.501***
0.887***
Currently in first marriage
REF
REF
REF
Full-time employed
-0.647***
0.337**
0.452**
Income (logged)
-0.047**
-0.053**
-0.017
Less than high school
-0.113
0.033
0.410
High school graduate
-0.380**
-0.024
0.328
Some college
-0.221
-0.189
0.278
College graduate or more
REF
REF
REF
Southern residence
-0.110
-0.417***
-0.253
Urban residence
-0.069
-0.095
-0.022
NH Black
-0.308**
0.544***
0.391*
Hispanic
-0.286*
0.330**
0.305
NH White
REF
REF
REF
Catholic
-0.242
0.179
0.184
Conservative Protestant
0.006
0.172
-0.133
Other religion
0.041
0.261
0.332
No religious affil.
-0.474*
0.022
-0.711
Mainline Protestant
REF
REF
REF
Attend church weekly
-0.099***
-0.068**
-0.072
T1 Depression Score
-0.005
0.006
-0.001
Health assessment at 50
0.373***
0.402***
0.614***
Results from Multinomial Treatment Models and Ordinary Least Squares Models
MTM
OLS
b
s.e.
b
s.e.
No parental roles
-0.803 0.139**
One parental role
--Two parental roles
-1.085 0.144***
Three or more parental roles
1.610 0.233***
Currently first married
Never-married
Previously-married
Cohabiting
Remarried
N
R-square (adjusted)
Chi-square
Log pseudo-likelihood
ln(σ)
Λ(no roles)
Λ(two roles)
Λ(three or more roles)
--0.983 0.174***
0.894 0.146***
0.303 0.146
0.358 0.198*
6,276
--3,346.56***
-23,879.53
1.199***
1.115***
1.502***
-1.113**
Model includes controls for female, employment, depression score at T1, education, residence,
race/ethnicity, religious affiliation, religious attendance, age 50 assessment
Results from Multinomial Treatment Models and Ordinary Least Squares Models
MTM
OLS
b
s.e.
b
s.e.
No parental roles
-0.803 0.139**
One parental role
--Two parental roles
-1.085 0.144***
Three or more parental roles
1.610 0.233***
Currently first married
Never-married
Previously-married
Cohabiting
Remarried
N
R-square (adjusted)
Chi-square
Log pseudo-likelihood
ln(σ)
Λ(no roles)
Λ(two roles)
Λ(three or more roles)
--0.983 0.174***
0.894 0.146***
0.303 0.146
0.358 0.198*
6,276
--3,346.56***
-23,879.53
1.199***
1.115***
1.502***
-1.113**
Model includes controls for female, employment, depression score at T1, education, residence,
race/ethnicity, religious affiliation, religious attendance, age 50 assessment
Results from Multinomial Treatment Models and Ordinary Least Squares Models
MTM
OLS
b
s.e.
b
s.e.
No parental roles
-0.803 0.139**
0.201
0.139
One parental role
----Two parental roles
-1.085 0.144***
0.223
0.137
Three or more parental roles
1.610 0.233***
0.718
0.232**
Currently first married
Never-married
Previously-married
Cohabiting
Remarried
N
R-square (adjusted)
Chi-square
Log pseudo-likelihood
ln(σ)
Λ(no roles)
Λ(two roles)
Λ(three or more roles)
--0.983 0.174***
0.894 0.146***
0.303 0.146
0.358 0.198*
6,276
--3,346.56***
-23,879.53
1.199***
1.115***
1.502***
-1.113**
--0.665
0.755
0.119
0.303
6,276
0.161
-------------
0.174***
0.146***
0.146
0.198*
Model includes controls for female, employment, depression score at T1, education, residence,
race/ethnicity, religious affiliation, religious attendance, age 50 assessment
Results from Multinomial Treatment Models and Ordinary Least Squares Models
MTM
OLS
b
s.e.
b
s.e.
No parental roles
-0.803 0.139**
0.201
0.139
One parental role
----Two parental roles
-1.085 0.144***
0.223
0.137
Three or more parental roles
1.610 0.233***
0.718
0.232**
Currently first married
Never-married
Previously-married
Cohabiting
Remarried
N
R-square (adjusted)
Chi-square
Log pseudo-likelihood
ln(σ)
Λ(no roles)
Λ(two roles)
Λ(three or more roles)
--0.983 0.174***
0.894 0.146***
0.303 0.146
0.358 0.198*
6,276
--3,346.56***
-23,879.53
1.199***
1.115***
1.502***
-1.113**
--0.665
0.755
0.119
0.303
6,276
0.161
-------------
0.174***
0.146***
0.146
0.198*
Model includes controls for female, employment, depression score at T1, education, residence,
race/ethnicity, religious affiliation, religious attendance, age 50 assessment
Comparison of Interaction Effects in MTM and OLS Regression
MTM
b
s.e.
No parental roles
-0.851
0.342*
One parental role
----Two parental roles
-1.390
0.304***
Three or more parental roles
0.856
0.852
Not first married (NFM)
0.560
0.184**
NFM * no roles
0.306
0.143*
NFM * two roles
0.267
0.133*
NFM * three or more roles
-0.586
0.453
N
6,276
R-square (adjusted)
--Chi-square
2,485.62 ***
Log pseudo-likelihood
22,690.85
ln(σ)
1.231 ***
Λ(no roles)
0.995 ***
Λ(two roles)
1.646 ***
Λ(three or more roles)
0.041
OLS
b
0.054
s.e.
0.237
0.017
0.924
0.436
0.280
0.310
-0.577
6,276
0.161
-------------
0.190
0.336***
0.177*
0.141*
0.133*
0.452
SOME CONCLUSIONS
 There are various ways to model selection—each with distinct advantages
and disadvantages
 MTM are useful when you have multiple treatments that you are trying to
compare
 Selection doesn’t always mean making significant variables non-significant!
 These models can take a while to fit in Stata.