MODELING SELECTION WITH MULTINOMIAL TREATMENT MODELS: AN EXAMPLE USING PARENTAL ROLES

KEVIN SHAFERSCHOOL OF SOCIAL WORKBRIGHAM 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

Person n’s subjective well-

beingSWB

SWB

SWB

SWB

SWB

Treated Not Treated

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.

Selection: unhappily married people tend to divorce, happily married people tend not to. Does this happiness level influence post-divorce SWB?

MULTINOMIAL TREATMENT MODELS

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

Married

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

roleTwo roles vs. One

roleThree or more

roles vs. One roleFemale -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 0.983 0.174*** Previously-married 0.894 0.146*** Cohabiting 0.303 0.146 Remarried 0.358 0.198* N 6,276 R-square (adjusted) --- Chi-square 3,346.56*** Log pseudo-likelihood -23,879.53 ln(σ) 1.199*** Λ(no roles) 1.115*** Λ(two roles) 1.502*** Λ(three or more roles) -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 0.983 0.174*** Previously-married 0.894 0.146*** Cohabiting 0.303 0.146 Remarried 0.358 0.198* N 6,276 R-square (adjusted) --- Chi-square 3,346.56*** Log pseudo-likelihood -23,879.53 ln(σ) 1.199*** Λ(no roles) 1.115*** Λ(two roles) 1.502*** Λ(three or more roles) -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 0.983 0.174*** 0.665 0.174***Previously-married 0.894 0.146*** 0.755 0.146***Cohabiting 0.303 0.146 0.119 0.146 Remarried 0.358 0.198* 0.303 0.198*N 6,276 6,276 R-square (adjusted) --- 0.161 Chi-square 3,346.56*** --- Log pseudo-likelihood -23,879.53 --- ln(σ) 1.199*** --- Λ(no roles) 1.115*** --- Λ(two roles) 1.502*** --- Λ(three or more roles) -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 0.983 0.174*** 0.665 0.174***Previously-married 0.894 0.146*** 0.755 0.146***Cohabiting 0.303 0.146 0.119 0.146 Remarried 0.358 0.198* 0.303 0.198*N 6,276 6,276 R-square (adjusted) --- 0.161 Chi-square 3,346.56*** --- Log pseudo-likelihood -23,879.53 --- ln(σ) 1.199*** --- Λ(no roles) 1.115*** --- Λ(two roles) 1.502*** --- Λ(three or more roles) -1.113** ---

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 OLS b s.e. b s.e. No parental roles -0.851 0.342* 0.054 0.237 One parental role --- --- Two parental roles -1.390 0.304*** 0.017 0.190 Three or more parental roles 0.856 0.852 0.924 0.336***Not first married (NFM) 0.560 0.184** 0.436 0.177*NFM * no roles 0.306 0.143* 0.280 0.141*NFM * two roles 0.267 0.133* 0.310 0.133*NFM * three or more roles -0.586 0.453 -0.577 0.452 N 6,276 6,276 R-square (adjusted) --- 0.161 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 ---

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.