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 Person n’s subjective well- being 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?

7. 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

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 T 1 depression score by year or initial age.  T 2 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: 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

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 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

12. 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

13. 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

14. 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

15. Logged Relative Risk of Number of Parental Roles from Stage 1 of MTM No roles vs. One role Two roles vs. One role Three or more roles vs. One role Female-0.925***0.070 -0.189 Never married3.435***-0.302 -0.118 Previously married1.903***-0.038 0.294 Cohabiting1.886***-0.027 -0.105 Remarried0.755***0.501***0.887*** Currently in first marriageREF 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 moreREF 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 WhiteREF Catholic-0.242 0.179 0.184 Conservative Protestant0.006 0.172 -0.133 Other religion0.041 0.261 0.332 No religious affil.-0.474*0.022 -0.711 Mainline ProtestantREF Attend church weekly-0.099***-0.068**-0.072 T1 Depression Score-0.005 0.006 -0.001 Health assessment at 500.373***0.402***0.614***

16. Results from Multinomial Treatment Models and Ordinary Least Squares Models MTM OLS bs.e. b No parental roles-0.8030.139** One parental role--- Two parental roles-1.0850.144*** Three or more parental roles1.6100.233*** Currently first married--- Never-married0.9830.174*** Previously-married0.8940.146*** Cohabiting0.3030.146 Remarried0.3580.198* N6,276 R-square (adjusted)--- Chi-square3,346.56*** 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

17. Results from Multinomial Treatment Models and Ordinary Least Squares Models MTM OLS bs.e. b No parental roles-0.8030.139** One parental role--- Two parental roles-1.0850.144*** Three or more parental roles1.6100.233*** Currently first married--- Never-married0.9830.174*** Previously-married0.8940.146*** Cohabiting0.3030.146 Remarried0.3580.198* N6,276 R-square (adjusted)--- Chi-square3,346.56*** 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

18. Results from Multinomial Treatment Models and Ordinary Least Squares Models MTM OLS bs.e. b No parental roles-0.8030.139** 0.2010.139 One parental role--- Two parental roles-1.0850.144*** 0.2230.137 Three or more parental roles1.6100.233*** 0.7180.232** Currently first married--- Never-married0.9830.174*** 0.6650.174*** Previously-married0.8940.146*** 0.7550.146*** Cohabiting0.3030.146 0.1190.146 Remarried0.3580.198* 0.3030.198* N6,276 R-square (adjusted)--- 0.161 Chi-square3,346.56*** --- 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

19. Results from Multinomial Treatment Models and Ordinary Least Squares Models MTM OLS bs.e. b No parental roles-0.8030.139** 0.2010.139 One parental role--- Two parental roles-1.0850.144*** 0.2230.137 Three or more parental roles1.6100.233*** 0.7180.232** Currently first married--- Never-married0.9830.174*** 0.6650.174*** Previously-married0.8940.146*** 0.7550.146*** Cohabiting0.3030.146 0.1190.146 Remarried0.3580.198* 0.3030.198* N6,276 R-square (adjusted)--- 0.161 Chi-square3,346.56*** --- 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

20. Comparison of Interaction Effects in MTM and OLS Regression MTM OLS bs.e. b No parental roles-0.8510.342* 0.0540.237 One parental role--- Two parental roles-1.3900.304*** 0.0170.190 Three or more parental roles0.8560.852 0.9240.336*** Not first married (NFM)0.5600.184** 0.4360.177* NFM * no roles0.3060.143* 0.2800.141* NFM * two roles0.2670.133* 0.3100.133* NFM * three or more roles-0.5860.453 -0.5770.452 N6,276 R-square (adjusted)--- 0.161 Chi-square2,485.62*** --- Log pseudo-likelihood22,690.85 --- ln(σ)1.231*** --- Λ(no roles)0.995*** --- Λ(two roles)1.646*** --- Λ(three or more roles)0.041 ---

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.