Modeling Selection with Multinomial Treatment Models: An Example Using Parental Roles

1. Modeling Selection with Multinomial Treatment Models: An Example Using Parental Roles Kevin Shafer School of Social Work Brigham Young University

2. 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.

3. 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

4. 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?

5. 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

6. A Basic Description of PSM Treated Not Treated Person n’s subjective well-being 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. 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

7. 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

8. 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)

9. Multinomial Treatment Model • Selection on the key independent variable • Two stage model: • Selection is modeled via a set of variables associated with entry into the independent variable • 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

10. 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%)

11. Stata code finditmtreatreg//to download command mtreatregd_t2 female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreqt2year,mtreat(nroles= female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreq t2year) sim(100) dens(normal) difficult

12. Stata code finditmtreatreg//to download command mtreatregd_t2 female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreqt2year, mtreat(nroles= female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreq t2year) sim(100) dens(normal) difficult

13. Stata code finditmtreatreg//to download command mtreatregd_t2 female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreqt2year,mtreat(nroles= female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreq t2year) sim(200) dens(normal) difficult

14. Stata code finditmtreatreg//to download command mtreatregd_t2 female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreqt2year,mtreat(nroles= female nmarpmar cohabit rm d_t1 emplylinc lhs hsgsc south urban black hispanic catholic cporelnoreligrelfreq t2year) sim(200) dens(normal) difficult

16. Model includes controls for female, employment, depression score at T1, education, residence, race/ethnicity, religious affiliation, religious attendance, age 50 assessment

17. Model includes controls for female, employment, depression score at T1, education, residence, race/ethnicity, religious affiliation, religious attendance, age 50 assessment

18. Model includes controls for female, employment, depression score at T1, education, residence, race/ethnicity, religious affiliation, religious attendance, age 50 assessment

19. Model includes controls for female, employment, depression score at T1, education, residence, race/ethnicity, religious affiliation, religious attendance, age 50 assessment

21. 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.