Modeling Selection with Multinomial Treatment Models: An Example
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Transcript Modeling Selection with Multinomial Treatment Models: An Example
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.