1. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 1 S052/II.2(a3): Applied Data Analysis Roadmap of the Course – What Is Today’s Topic Area? © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a2) – Slide 1 More details can be found in the “Course Objectives and Content” handout on the course webpage. Multiple Regression Analysis (MRA) Multiple Regression Analysis (MRA) Do your residuals meet the required assumptions? Test for residual normality Use influence statistics to detect atypical datapoints If your residuals are not independent, replace OLS by GLS regression analysis Use Individual growth modeling Specify a Multi-level Model If your sole predictor is continuous, MRA is identical to correlational analysis If your sole predictor is dichotomous, MRA is identical to a t-test If your several predictors are categorical, MRA is identical to ANOVA If time is a predictor, you need discrete- time survival analysis… If your outcome is categorical, you need to use… Binomial logistic regression analysis (dichotomous outcome) Multinomial logistic regression analysis (polytomous outcome) If you have more predictors than you can deal with, Create taxonomies of fitted models and compare them. Form composites of the indicators of any common construct. Conduct a Principal Components Analysis Use Cluster Analysis Use non-linear regression analysis. Transform the outcome or predictor If your outcome vs. predictor relationship is non-linear, How do you deal with missing data? Today’s Topic Area

2. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 2 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Printed Syllabus – What Is Today’s Topic? Please check inter-connections among the Roadmap, the Daily Topic Area, the Printed Syllabus, and the content of today’s class when you pre-read the day’s materials. Today, in the third part of Syllabus Section II.2(a), on Discrete-Time Survival Analysis, I will: Demonstrate how a substantive predictor can be included in the discrete-time hazard (DTSA) model (#4-#14). Show how standard methods of logistic regression analysis can be used to test and interpret the ensuing DTSA models (#15-#19). Contrast life-table and DTSA estimates of a predictor’s main effect (#20). Comment on important extensions of the basic DTSA approach (#21). Today, in the third part of Syllabus Section II.2(a), on Discrete-Time Survival Analysis, I will: Demonstrate how a substantive predictor can be included in the discrete-time hazard (DTSA) model (#4-#14). Show how standard methods of logistic regression analysis can be used to test and interpret the ensuing DTSA models (#15-#19). Contrast life-table and DTSA estimates of a predictor’s main effect (#20). Comment on important extensions of the basic DTSA approach (#21).

3. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 3 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Three Kinds Of Survival Analysis Classical Methods of Survival Analysis  Simple data-analytic approaches for summarizing survival data appropriately: sample hazard functionEstimation of the sample hazard function. sample survivor functionEstimation of the sample survivor function. median lifetime.Estimation of the median lifetime.  Simple tests of differences in survivor function, by “group”: Survival analytic equivalent of the t-test. Classical Methods of Survival Analysis  Simple data-analytic approaches for summarizing survival data appropriately: sample hazard functionEstimation of the sample hazard function. sample survivor functionEstimation of the sample survivor function. median lifetime.Estimation of the median lifetime.  Simple tests of differences in survivor function, by “group”: Survival analytic equivalent of the t-test. Last Time Discrete-Time Survival Analysis  Easily replicates classical methods of survival analysis, using logistic regression analysis.  Reframes classical survival analytic methods in a regression format: Permits the inclusion of multiple predictors, including interactions. Provides testing with the Wald test & differences in the –2LL statistic. Fitted hazard & survivor functions, & median lifetimes, are easily recovered from the fitted logistic model.Discrete-Time Survival Analysis  Easily replicates classical methods of survival analysis, using logistic regression analysis.  Reframes classical survival analytic methods in a regression format: Permits the inclusion of multiple predictors, including interactions. Provides testing with the Wald test & differences in the –2LL statistic. Fitted hazard & survivor functions, & median lifetimes, are easily recovered from the fitted logistic model. Last Time, & Today Continuous-Time Survival Analysis  A replacement for discrete-time survival analysis when time has been measured continuously.  Imposes additional assumptions on the data.  Reframes classical survival analytic methods in a regression format: Permits the inclusion of predictors, including interactions. Accompanied by its own testing procedures, based on standard practices. Fitted hazard & survivor functions, & median lifetimes, are easily recovered from fitted models.Continuous-Time Survival Analysis  A replacement for discrete-time survival analysis when time has been measured continuously.  Imposes additional assumptions on the data.  Reframes classical survival analytic methods in a regression format: Permits the inclusion of predictors, including interactions. Accompanied by its own testing procedures, based on standard practices. Fitted hazard & survivor functions, & median lifetimes, are easily recovered from fitted models. Next year, … ?

4. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 4 New data example … data described in FIRSTSEX_PP_info.pdf ….FIRSTSEX_PP_info.pdf New data example … data described in FIRSTSEX_PP_info.pdf ….FIRSTSEX_PP_info.pdf 822 person-period records.Sample size Singer & Willett, 2003Singer & Willett, 2003, Chapter 11.More Info Capaldi, D. M., Crosby, L., & Stoolmiller, M. (1996). Predicting The Timing Of First Sexual Intercourse For At-Risk Adolescent Males. Child Development, 67, 344-359. Source A person-period dataset recording the high-school grade (7 th – 12 th ) in which at-risk adolescent boys experienced heterosexual sex for the first time, with information on: 1.Whether the boy had experienced a parental transition during early childhood (eg., a parental divorce and/or a parental death prior to 7 th grade). 2.The parents’ level of antisocial behavior during the boy’s early childhood. Overview FIRSTSEX_PP.txtDataset S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model New Data Example … Adolescent Boy’s First Experience Of Heterosexual Sex Research Questions 1.Whether, and if so in which grade, at-risk adolescent boys first experience heterosexual sex? 2.How the risk of first heterosexual sex depends on the boy’s experiences with parental death and divorce in early childhood? Research Questions 1.Whether, and if so in which grade, at-risk adolescent boys first experience heterosexual sex? 2.How the risk of first heterosexual sex depends on the boy’s experiences with parental death and divorce in early childhood?

5. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 5 ColVarVariable DescriptionLabels 1IDAdolescent identification code.Integer 2GRADEGrade to which this person-period record refers.Integer, between 7 and 12. 3EVENT Dummy variable indicating whether the boy experienced first heterosexual sex in this grade. 0 = no,1 = yes. 4G7Is this time-period Grade 7?0 = no,1 = yes. 5G8Is this time-period Grade 8?0 = no,1 = yes. 6G9Is this time-period Grade 9?0 = no,1 = yes. 7G10Is this time-period Grade 10?0 = no,1 = yes. 8G11Is this time-period Grade 11?0 = no,1 = yes. 9G12Is this time-period Grade 12?0 = no,1 = yes. 10PT Did the boy experience one or more parenting transitions (death or divorce) prior to 7 th grade? 0 = no,1 = yes. 11PAS Parents’ level of antisocial behavior during the boy’s early childhood. Continuous variable, mean zero, ranges from –1.7 to 2.8 in the full sample. S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Person-Period Dataset – Adolescent Boy’s Age At First Heterosexual Sex Two representations of time: 1.GRADE indicates a boy’s HS grade in each discrete-time period. 2.G7 through G12 convert GRADE into a system of dichotomous time indictors for use in specifying a discrete-time hazard model. Two representations of time: 1.GRADE indicates a boy’s HS grade in each discrete-time period. 2.G7 through G12 convert GRADE into a system of dichotomous time indictors for use in specifying a discrete-time hazard model. The outcome variable is a dichotomous event indicator, whose value indicates whether the boy’s first experience of heterosexual sex occurs in each discrete time period There are actually two potentially interesting predictors, but we will focus initially on the effect of parental transitions, PT.

6. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 6 *---------------------------------------------------------------------* Input the FIRSTSEX person-period dataset *---------------------------------------------------------------------*; DATA FIRSTSEX_PP; INFILE 'C:\DATA\S052\FIRSTSEX_PP.txt'; INPUT ID GRADE EVENT G7-G12 PT PAS; LABEL ID = 'Identification Code' GRADE = 'Grade' EVENT = 'Did Boy Have Heterosexual Sex for the First Time?' PT = 'Did Boy Experience Early Parenting Transitions?' PAS = 'Parents Level of Antisocial Behavior in Childhood'; PROC FORMAT; VALUE EFMT 0='No' 1='Yes'; VALUE PTFMT 0='No' 1='Yes'; *---------------------------------------------------------------------* Examining the person-period data *---------------------------------------------------------------------*; PROC PRINT DATA=FIRSTSEX_PP (OBS=40); VAR ID GRADE EVENT PT; FORMAT EVENT EFMT. PT PTFMT.; *---------------------------------------------------------------------* Conducting the Life Table Analysis, time-only analysis *---------------------------------------------------------------------*; PROC FREQ DATA=FIRSTSEX_PP; TABLE GRADE*EVENT / NOCOL NOPCT; FORMAT EVENT EFMT. PT PTFMT.; *---------------------------------------------------------------------* Input the FIRSTSEX person-period dataset *---------------------------------------------------------------------*; DATA FIRSTSEX_PP; INFILE 'C:\DATA\S052\FIRSTSEX_PP.txt'; INPUT ID GRADE EVENT G7-G12 PT PAS; LABEL ID = 'Identification Code' GRADE = 'Grade' EVENT = 'Did Boy Have Heterosexual Sex for the First Time?' PT = 'Did Boy Experience Early Parenting Transitions?' PAS = 'Parents Level of Antisocial Behavior in Childhood'; PROC FORMAT; VALUE EFMT 0='No' 1='Yes'; VALUE PTFMT 0='No' 1='Yes'; *---------------------------------------------------------------------* Examining the person-period data *---------------------------------------------------------------------*; PROC PRINT DATA=FIRSTSEX_PP (OBS=40); VAR ID GRADE EVENT PT; FORMAT EVENT EFMT. PT PTFMT.; *---------------------------------------------------------------------* Conducting the Life Table Analysis, time-only analysis *---------------------------------------------------------------------*; PROC FREQ DATA=FIRSTSEX_PP; TABLE GRADE*EVENT / NOCOL NOPCT; FORMAT EVENT EFMT. PT PTFMT.; In Data Analytic Handout II.2(a).4, I conduct preliminary life-table analyses, first for the whole sample … S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Life-Table Analysis For The Full Sample Of Adolescent Boys Standard input, labeling and formatting statements Print out a few cases for inspection Conduct a full-sample life table analysis

7. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 7 ID GRADE EVENT PT 1 7 No No 1 8 No No 1 9 Yes No 2 7 No Yes 2 8 No Yes 2 9 No Yes 2 10 No Yes 2 11 No Yes 2 12 No Yes 3 7 No No 3 8 No No 3 9 No No 3 10 No No 3 11 No No 3 12 No No 5 7 No Yes 5 8 No Yes 5 9 No Yes 5 10 No Yes 5 11 No Yes 5 12 Yes Yes 6 7 No No 6 8 No No 6 9 No No 6 10 No No 6 11 Yes No ID GRADE EVENT PT 1 7 No No 1 8 No No 1 9 Yes No 2 7 No Yes 2 8 No Yes 2 9 No Yes 2 10 No Yes 2 11 No Yes 2 12 No Yes 3 7 No No 3 8 No No 3 9 No No 3 10 No No 3 11 No No 3 12 No No 5 7 No Yes 5 8 No Yes 5 9 No Yes 5 10 No Yes 5 11 No Yes 5 12 Yes Yes 6 7 No No 6 8 No No 6 9 No No 6 10 No No 6 11 Yes No S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Person-Period Dataset For The FIRSTSEX Dataset  Boy #3 was observed from 7 th thru 12 th Grade but he never experienced the event of interest during that time, and was therefore censored.  Neither did he suffer a parental transition during early childhood.  Boy #3 was observed from 7 th thru 12 th Grade but he never experienced the event of interest during that time, and was therefore censored.  Neither did he suffer a parental transition during early childhood.  Boy #1 experienced heterosexual sex for the first time in 9 th Grade.  There were no parental transitions in his early life.  Boy #1 experienced heterosexual sex for the first time in 9 th Grade.  There were no parental transitions in his early life.  Boy #5 experienced heterosexual sex for the first time in 12 th grade,  He also weathered a parental transition in early childhood.  Boy #5 experienced heterosexual sex for the first time in 12 th grade,  He also weathered a parental transition in early childhood.

8. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 8 GRADE EVENT Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 165 ‚ 15 ‚ 180 ‚ 91.67 ‚ 8.33 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 158 ‚ 7 ‚ 165 ‚ 95.76 ‚ 4.24 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 134 ‚ 24 ‚ 158 ‚ 84.81 ‚ 15.19 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 105 ‚ 29 ‚ 134 ‚ 78.36 ‚ 21.64 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 80 ‚ 25 ‚ 105 ‚ 76.19 ‚ 23.81 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 54 ‚ 26 ‚ 80 ‚ 67.50 ‚ 32.50 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 696 126 822 GRADE EVENT Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 165 ‚ 15 ‚ 180 ‚ 91.67 ‚ 8.33 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 158 ‚ 7 ‚ 165 ‚ 95.76 ‚ 4.24 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 134 ‚ 24 ‚ 158 ‚ 84.81 ‚ 15.19 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 105 ‚ 29 ‚ 134 ‚ 78.36 ‚ 21.64 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 80 ‚ 25 ‚ 105 ‚ 76.19 ‚ 23.81 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 54 ‚ 26 ‚ 80 ‚ 67.50 ‚ 32.50 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 696 126 822 HS Grade t Estimated h(t) Estimated S(t) 6-- 1.0000 70.0833 (1 - 0.0833)  1.0000 = 0.9167 80.0424 (1 - 0.0424)  0.9167= 0.8778 90.1519 (1 - 0.1519)  0.8778= 0.7444 100.2164 (1 - 0.2164)  0.7444= 0.5833 110.2381 (1 - 0.2381)  0.5833 = 0.4444 120.3250 (1 - 0.3250)  0.4444= 0.3000 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Life Table Analysis For The Full Sample Of Adolescent Boys Sample Life Table Analysis Sample Hazard and Survivor Functions

9. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 9 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Sample Hazard & Survivor Functions For The Full Sample Of Adolescent Boys The risk of the first experience of heterosexual sex for these at-risk boys rises throughout the high school grades. By linear interpolation, the median grade of the first experience of heterosexual sex for these at-risk boys is about two-thirds of the way through 10 th grade (actually 10.6).

10. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 10 *---------------------------------------------------------------* Conducting the Life Table Analysis, separately by levels of PT *---------------------------------------------------------------*; PROC SORT; BY PT; PROC FREQ DATA=FIRSTSEX_PP; BY PT; TABLE GRADE*EVENT / NOCOL NOPCT; FORMAT EVENT EFMT. PT PTFMT.; *---------------------------------------------------------------* Conducting the Life Table Analysis, separately by levels of PT *---------------------------------------------------------------*; PROC SORT; BY PT; PROC FREQ DATA=FIRSTSEX_PP; BY PT; TABLE GRADE*EVENT / NOCOL NOPCT; FORMAT EVENT EFMT. PT PTFMT.; In Data Analytic Handout II.2(a).4, I also conducted exploratory life-table analyses intended to reveal how predictor PT seems to impact the risk of first heterosexual intercourse … S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Life Table Analysis, by Parental Transition, In PC-SAS Sort the person-period data, by PT Conduct a life table analysis, separately by levels of parental transition, PT.

11. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 11 GRADE(Grade) EVENT (Sex?) Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 70 ‚ 2 ‚ 72 ‚ 97.22 ‚ 2.78 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 68 ‚ 2 ‚ 70 ‚ 97.14 ‚ 2.86 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 60 ‚ 8 ‚ 68 ‚ 88.24 ‚ 11.76 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 52 ‚ 8 ‚ 60 ‚ 86.67 ‚ 13.33 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 42 ‚ 10 ‚ 52 ‚ 80.77 ‚ 19.23 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 34 ‚ 8 ‚ 42 ‚ 80.95 ‚ 19.05 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 326 38 364 GRADE(Grade) EVENT (Sex?) Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 70 ‚ 2 ‚ 72 ‚ 97.22 ‚ 2.78 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 68 ‚ 2 ‚ 70 ‚ 97.14 ‚ 2.86 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 60 ‚ 8 ‚ 68 ‚ 88.24 ‚ 11.76 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 52 ‚ 8 ‚ 60 ‚ 86.67 ‚ 13.33 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 42 ‚ 10 ‚ 52 ‚ 80.77 ‚ 19.23 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 34 ‚ 8 ‚ 42 ‚ 80.95 ‚ 19.05 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 326 38 364 For boys who experienced no parenting transition in early childhood (PT=0) … GRADE(Grade) EVENT (Sex?) Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 95 ‚ 13 ‚ 108 ‚ 87.96 ‚ 12.04 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 90 ‚ 5 ‚ 95 ‚ 94.74 ‚ 5.26 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 74 ‚ 16 ‚ 90 ‚ 82.22 ‚ 17.78 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 53 ‚ 21 ‚ 74 ‚ 71.62 ‚ 28.38 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 38 ‚ 15 ‚ 53 ‚ 71.70 ‚ 28.30 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 20 ‚ 18 ‚ 38 ‚ 52.63 ‚ 47.37 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 370 88 458 GRADE(Grade) EVENT (Sex?) Frequency ‚ Row Pct ‚ No ‚ Yes ‚ Total ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 7 ‚ 95 ‚ 13 ‚ 108 ‚ 87.96 ‚ 12.04 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 8 ‚ 90 ‚ 5 ‚ 95 ‚ 94.74 ‚ 5.26 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 9 ‚ 74 ‚ 16 ‚ 90 ‚ 82.22 ‚ 17.78 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 10 ‚ 53 ‚ 21 ‚ 74 ‚ 71.62 ‚ 28.38 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 11 ‚ 38 ‚ 15 ‚ 53 ‚ 71.70 ‚ 28.30 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ 12 ‚ 20 ‚ 18 ‚ 38 ‚ 52.63 ‚ 47.37 ‚ ƒƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆƒƒƒƒƒƒƒƒˆ Total 370 88 458 For boys who did experience a parenting transition in early childhood (PT=1) … S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Sample Life Tables, by Parental Transition What’s the difference?

12. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 12 Boys who were subject to a parental transition in early childhood are consistently at greater risk of experiencing first heterosexual sex in all grades PT=0 PT=1 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Sample Hazard Functions, by Parental Transition

13. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 13 The median time to first heterosexual sex is almost two years shorter for boys who were subject to a parental transition in early childhood than for boys who experienced no parental transition (9.95 vs. 11.75) PT=0 PT=1 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Sample Survivor Functions, by Parental Transition

14. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 14 *--------------------------------------------------------------------* Input the person-period dataset *--------------------------------------------------------------------*; DATA FIRSTSEX_PP; INFILE 'C:\DATA\S052\FIRSTSEX_PP.txt'; INPUT ID GRADE EVENT G7-G12 PT PAS; LABEL ID = 'Identification Code' GRADE = 'Grade' EVENT = 'Did Boy Have Heterosexual Sex for First Time?' PT = 'Did Boy Experience Early Parenting Transitions?' PAS = 'Parents Antisocial Behavior in Childhood'; PROC FORMAT; VALUE EFMT0='No' 1='Yes'; *--------------------------------------------------------------------* Fitting the discrete-time hazard model, including PT as a predictor *--------------------------------------------------------------------*; PROC LOGISTIC DATA=FIRSTSEX_PP; FORMAT EVENT EFMT.; MODEL EVENT(event='Yes') = G7-G12 / NOINT ; PROC LOGISTIC DATA=FIRSTSEX_PP; FORMAT EVENT EFMT.; MODEL EVENT(event='Yes') = G7-G12 PT / NOINT ; *--------------------------------------------------------------------* Input the person-period dataset *--------------------------------------------------------------------*; DATA FIRSTSEX_PP; INFILE 'C:\DATA\S052\FIRSTSEX_PP.txt'; INPUT ID GRADE EVENT G7-G12 PT PAS; LABEL ID = 'Identification Code' GRADE = 'Grade' EVENT = 'Did Boy Have Heterosexual Sex for First Time?' PT = 'Did Boy Experience Early Parenting Transitions?' PAS = 'Parents Antisocial Behavior in Childhood'; PROC FORMAT; VALUE EFMT0='No' 1='Yes'; *--------------------------------------------------------------------* Fitting the discrete-time hazard model, including PT as a predictor *--------------------------------------------------------------------*; PROC LOGISTIC DATA=FIRSTSEX_PP; FORMAT EVENT EFMT.; MODEL EVENT(event='Yes') = G7-G12 / NOINT ; PROC LOGISTIC DATA=FIRSTSEX_PP; FORMAT EVENT EFMT.; MODEL EVENT(event='Yes') = G7-G12 PT / NOINT ; In Data-Analytic Handout II.2(a).5, I fit discrete-time hazard models to these data … S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Fitting A Short Taxonomy Of DTSA Models In PC-SAS Standard input, labeling and formatting statements Fitting a “time-only” discrete-time hazard model Adding the main effect of PT

15. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 15 -2LL PT G12 G11 G10 G9 G8 G7 634.66651.961139.53 0.874*** -1.179***-0.731** -1.654***-1.163*** -1.823***-1.287*** -2.281***-1.720*** -3.700***-3.117*** -2.994***-2.398*** Including PTTime-onlyNull Fitted Discrete-Time Hazard Model S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model A Fitted Taxonomy of DTSA Models Conclusion: Main effect of HS Grade is an important 1 st predictor of risk of first heterosexual intercourse. Conclusion: Main effect of PT is an important 2 nd predictor of risk of first heterosexual intercourse.

16. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 16 -2LL PT G12 G11 G10 G9 G8 G7 634.66651.961139.53 0.874*** -1.179***-0.731** -1.654***-1.163*** -1.823***-1.287*** -2.281***-1.720*** -3.700***-3.117*** -2.994***-2.398*** Including PTTime-onlyNull Fitted Discrete-Time Hazard Model S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Interpreting Fitted Parameters Directly Using Odds-Ratios These parameter estimates provide a fitted logit hazard function for a “baseline” group of boys, for whom the predictor PT equals 0. This parameter estimate “elevates” the fitted logit-hazard profile for boys who experienced an early parental transition: “The fitted odds that a boy whose parents die or divorce prior to 7 th grade will first experience heterosexual sex (vs. not having sex) are 2.4 times the odds for a boy whose parents do not undergo such a transition.” This parameter estimate “elevates” the fitted logit-hazard profile for boys who experienced an early parental transition: “The fitted odds that a boy whose parents die or divorce prior to 7 th grade will first experience heterosexual sex (vs. not having sex) are 2.4 times the odds for a boy whose parents do not undergo such a transition.”

17. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 17 You can easily construct prototypical fitted hazard functions by substituting substantively-interesting values of the predictors into the fitted logistic regression model … For boys who experienced no early parental transitions (PT=0): For boys who experienced an early parental transition (PT=1): And then plot these prototypical functions, as usual … S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Plotting Fitted Hazard Functions For Prototypical Adolescent Boys

18. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 18 PT=0 PT=1 Based on the fitted discrete-time hazard model: 1.Risk of first heterosexual sex generally increases with grade for all boys, 2.Boys whose parents have divorced or died in early childhood are at greater risk of experiencing first heterosexual sex at every grade. Based on the fitted discrete-time hazard model: 1.Risk of first heterosexual sex generally increases with grade for all boys, 2.Boys whose parents have divorced or died in early childhood are at greater risk of experiencing first heterosexual sex at every grade. S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Fitted Hazard Functions For Prototypical Adolescent Boys

19. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 19 PT=1 Based on the fitted discrete-time hazard model:  Half of the boys with parenting transitions in early childhood first experience heterosexual sex by tenth grade (9.93).  Half of the boys with no parenting transitions in early childhood first experience heterosexual sex by twelfth grade (11.76). Based on the fitted discrete-time hazard model:  Half of the boys with parenting transitions in early childhood first experience heterosexual sex by tenth grade (9.93).  Half of the boys with no parenting transitions in early childhood first experience heterosexual sex by twelfth grade (11.76). PT=0 S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Fitted Survivor Functions For Prototypical Adolescent Boys

20. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 20 PT=0 PT=1 PT=0 PT=1 Life-table estimates of hazard DTSA-fitted estimates of hazard S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Comparing Estimated Hazard Functions From The Life-Table and DTSA Approaches Similar, but not identical – Similar, but not identical – why is that, what’s the natural next model to fit?

21. © Willett, Harvard University Graduate School of Education, 6/13/2016S052/II.2(a3) – Slide 21 You can include interactions between substantive predictors and time: This is called “testing the proportional-odds assumption.” You can add more substantive predictors to the basic DTSA model: Main effects of substantive predictors, Interactions among substantive predictors. You can include time-varying predictors. Easy to record their values in the person-period dataset. Easy to insert into the DTSA model. You can replace the completely general specification for time with more parsimonious specifications of time: Transformations, polynomials. Non-linear functions. Discontinuous functions. You can model the impact of competing events. You can conduct analyses of multiple-spells. Repetitions of a single event. Alternating events. You can switch to continuous-time survival analysis. You can keep a more careful watch on the boys that your teenage daughters date (perhaps even enquiring whether their parents experienced early “transitions” in their marriage?) You can include interactions between substantive predictors and time: This is called “testing the proportional-odds assumption.” You can add more substantive predictors to the basic DTSA model: Main effects of substantive predictors, Interactions among substantive predictors. You can include time-varying predictors. Easy to record their values in the person-period dataset. Easy to insert into the DTSA model. You can replace the completely general specification for time with more parsimonious specifications of time: Transformations, polynomials. Non-linear functions. Discontinuous functions. You can model the impact of competing events. You can conduct analyses of multiple-spells. Repetitions of a single event. Alternating events. You can switch to continuous-time survival analysis. You can keep a more careful watch on the boys that your teenage daughters date (perhaps even enquiring whether their parents experienced early “transitions” in their marriage?) S052/II.2(a3): Extensions of Basic DSTA Approach/Adding Predictors To The Model Extensions Of The DSTA Approach