1 & 1 Workshop: Latent Transition Analysis Bethany C. Bray Associate Director, The Methodology Center 29 March 2018 methodology.psu.edu bethanycbray.wordpress.com

Overview of workshop Conceptual introduction to LCA + LTA An in-depth example of LTA Adding grouping variables Predicting membership + transitions

Conceptual introduction to LCA + LTA

Some basic ideas of LCA Individuals can be divided into subgroups, or latent classes, based on unobserved construct True class membership is unknown Latent classes are mutually exclusive and exhaustive

Some basic ideas of LCA Measurement of construct (i.e., latent variable) based on several categorical indicators There is error associated with measurement of the latent classes Similar to factor analysis, but latent variable is categorical

An example of LCA Eight indicators of adolescent depression (28 = 256 possible response patterns) SAD Could not shake blues Felt depressed Felt lonely Felt sad DISLIKED People unfriendly Disliked by people FAILURE Life was failure Life not worth living

An example of LCA Five latent classes of depression were identified Prevalence No depression 41% Sad 18% Disliked 17% Sad and disliked 15% Depressed 9%

An example of LCA Probability of ‘yes’ conditional on latent class membership Indicator Class 1: Class 2: Class 3: Class 4: Class 5: Non-dep Sad Disliked S + D Dep Could not shake blues .03 .54 .17 .66 .90 Felt depressed .06 .73 .24 .86 1.00 Felt lonely .07 .58 .33 .77 .92 Felt sad .14 .80 .38 .87 .94 People unfriendly .13 .64 .67 .70 People dislike you .04 .00 .68 Life was failure .01 .11 .10 .23 Not worth living .85

An example of LCA Interested in… Latent class prevalences e.g., probability of membership in DEPRESSED class Item-response probabilities e.g., probability of reporting FELT LONELY given membership in DEPRESSED class

Some basic ideas of LTA LTA is a longitudinal extension of LCA Development can be represented as movement through discrete categories or stages Error associated with the measurement of the discrete categories or stages

Some basic ideas of LTA Different individuals may take different paths Heterogeneity in movement is unobserved (i.e., latent)

LTA Provides a way to estimate and test models of stage- sequential development In LCA, the classes are static In LTA, the classes are dynamic Sometimes, we refer to the dynamic latent classes as latent statuses

LTA Estimates prevalences of latent statuses and incidences of transitions between latent statuses over time, adjusted for measurement error

LTA Latent Status 2 Latent Status 1 Latent Status 4 Latent Status 3

LTA Depression Depression Classes at Time 2 Classes at Time 1 Life not worth living Depression Classes at Time 1 Could not shake the blues … Life not worth living Depression Classes at Time 2 Could not shake the blues …

LTA So, now we are also interested in… Transition probabilities e.g., probability of membership in DEPRESSED class at Time 2 conditional on membership in the SAD + DISLIKED class at Time 1

LTA Time 2 Time 1 Class 1: Class 2: Class 3: Class 4: Class 5: Non-Dep Sad Disliked S + D Dep Class 1: Non-Depressed .77 .12 .09 .02 .01 Class 2: Sad .33 .49 .07 .05 Class 3: Disliked .24 .08 .46 .16 .06 Class 4: Sad + Disliked .22 .28 .40 .10 Class 5: Depressed .00 .13 .58

Ideas underlying LTA LTA provides a way of fitting models with these characteristics: Change is discrete Data are longitudinal (2 or more times) Measurement error Heterogeneity in development

Latent classes of sexual risk behavior

Sexual risk behavior over time Goal: To model change over time in dating and sexual risk behavior among adolescents and young adults From Lanza and Collins (2008) in Developmental Psychology

We will use LTA to… Fit a developmental model of dating and sexual risk behavior across 3 time Examine… Latent structure of dating and sexual risk behavior How many latent statuses? What is their interpretation? Prevalence of latent statuses at each time Transition probabilities (T1 to T2, T2 to T3)

Participants National Longitudinal Survey of Youth 1997 (NLSY97) Our sample… US high school students aged 17 or 18 at Time 1 n = 2937 (49% female) Assessed in 1998, 1999, 2000 Married participants not included

Indicators of behavior DATING PARTNERS number of dating partners in the past year SEXUAL PARTNERS # of sexual partners in past year 1=zero, 2=one, 2=two or more 1=zero, 2=one, 3=two or more PAST-YEAR SEX EXPOSED At least 1 instance of intercourse w/0 a condom (i.e., exposure to STI’s) in past year 1=no, 2=yes

Now, we will… Use LTA to identify and describe underlying classes of dating and sexual risk Use LTA to examine transitions between underlying classes of dating and sexual risk

The 5-class model Indicator Status 1 Status 2 Status 3 Status 4 # Dating Partners .76 (0) .18 (1) .06 (2+) .01 (0) .20 (1) .79 (2+) .10 (0) .66 (1) .24 (2+) .05 (0) .03 (1) .93 (2+) .02 (0) .05 (1) Past-year Sex .98 (No) .02 (Yes) .00 (No) 1.00 (Yes) # Sex 1.00 (0) .00 (1) .00 (2+) .00 (0) .97 (1) .03 (2+) .34 (1) .64(2+) .09 (1) .91 (2+) Exposed to STD 1.00 (No) .00 (Yes) .40 (No) .60 (Yes) .82 (No) .18 (Yes) .19 (No) .81 (Yes)

Labeling the 5 classes Indicator Status 1 Status 2 Status 3 Status 4 Non-Daters Daters Mono-gamous Multi-part Safe Multi-part Exposed # Dating Partners √ (0) √ (2+) √ (1) Past-year Sex √ (No) √ (Yes) # Sex Exposed to STD

Prevalences at each time Non- Daters Monog- amous Multi-part Safe Exposed Time 1 .19 .29 .12 .23 .18 Time 2 .13 .22 .21 Time 3 .11 .17 .25

Change over time Non- daters Daters Monog- amous Multi-part Safe Exposed Non-daters .61 .64 .18 .15 .08 .09 .06 .03 .00 .01 .04 .57 .53 .16 .19 .21 .17 .05 Monog-amous .68 .66 .14 .24 .11 .10 .54 .02 .25 .81 .72

Change over time Non- daters Daters Monog- amous Multi-part Safe Exposed Non-daters .61 .64 .18 .15 .08 .09 .06 .03 .00 .01 .04 .57 .53 .16 .19 .21 .17 .05 Monog-amous .68 .66 .14 .24 .11 .10 .54 .02 .25 .81 .72

Change over time Non- daters Daters Monog- amous Multi-part Safe Exposed Non-daters .61 .64 .18 .15 .08 .09 .06 .03 .00 .01 .04 .57 .53 .16 .19 .21 .17 .05 Monog-amous .68 .66 .14 .24 .11 .10 .54 .02 .25 .81 .72

Change over time Non- daters Daters Monog- amous Multi-part Safe Exposed Non-daters .61 .64 .18 .15 .08 .09 .06 .03 .00 .01 .04 .57 .53 .16 .19 .21 .17 .05 Monog-amous .68 .66 .14 .24 .11 .10 .54 .02 .25 .81 .72

Summary of findings Increasing membership in the Monogamous and Multi-Partner Exposed (i.e., highest risk) latent statuses over time Membership in the Multi-Partner Exposed latent status is the most stable over time

Summary of findings Members of the Monogamous latent status were the most likely to transition to Multi-Partner Exposed at the next time No one in the Multi-Partner Exposed latent status was expected to transition to the Multi-Partner Safe latent status

Other examples of LTA in the Literature

Other examples of LTA in literature Transitions in first-year college student drinking behaviors (Cleveland et al., 2012) Non-drinkers (42% to 30%) Weekend Non-Bingers (20% to 19%) Weekend Bingers (30% to 22%) Heavy Drinkers (8% to 28%) Also examined intervention effects on transitions!

Other examples of LTA in literature Transitions in eating disorder phenotypes in a clinical sample (Castellini et al., 2013) Severe Binging Moderate Binging Restricted Eating Binge + Moderate Purging Binge + Severe Purging

Other examples of LTA in literature Stages of change and sequential stage transitions for smoking acquisition and cessation among adolescents (Guo et al., 2009) Precontemplation Contemplation Preparation Action Maintenance

Other examples of LTA in literature Changes in social information processing of aggression predicted by community violence exposure, aggressive behavior, and behavior regulation (Goldweber et al., 2011) Stable low SIP Decreasing SIP Increasing SIP Stable high SIP

Other examples of LTA in literature Transitions in risk for HIV among young injection drug users (Mackesy-Amiti et al., 2013) Low risk Non-syringe equipment-sharing Moderate-risk syringe-sharing High-risk syringe-sharing Intervention moved individuals from high-risk to low-risk class

Other examples of LTA in literature Transitions between classes of meeting or not meeting the Healthy People 2010 recommendations for participation in regular moderate or vigorous physical exercise (Dishman, DeJoy, Wilson, & Vandenberg, 2009) The intervention significantly increased the proportion of individuals meeting the recommendations

More about transition parameters

More about transition parameters τ parameters arranged in a transition probability matrix Time 2 τb|a = Time 1

More about transition parameters τ parameters can be restricted in a variety of ways to test interesting hypotheses about development

More about transition parameters For example, a model of ‘no backsliding’ would have a transition matrix like below Time 2 τb|a = Time 1

More about transition parameters For example, a model of ‘no change’ would have a transition matrix like below Time 2 τb|a = Time 1

Adding grouping variables

Extending our study… …of dating and sexual risk behavior Additional goal of the study: to examine gender differences in dating and sexual risk behavior

Multiple-groups LTA Reasons to include a grouping variable: To explore measurement invariance “Do the items map onto the latent construct in the same way for males and females?”

Multiple-groups LTA Reasons to include a grouping variable: To divide sample into groups for comparison purposes “How does the probability of membership in the MONOGAMOUS latent class differ in the experimental and control groups?” “How does the probability of transitioning to the high-risk status differ between males and females?”

Gender differences at Time 1 Behavior Status Males Females Non-daters .17 .20 Daters .28 .30 Monogamous .08 .18 Multi-partner safe .16 Multi-partner exposed

Additional research questions Possible grouping variables might include… Poverty below threshold Pubertal status (early vs. on-time vs. late) Treatment group

Additional research questions Example research questions: Are children in households with low income more likely to be engaging in risky sexual behavior at Time 1? Are females with early pubertal timing more likely to transition to risky sexual behavior than their on-time or late pubertal timing counterparts?

Predicting membership + transitions

Extending our study… …of dating and sexual risk behavior Additional goals of study: to predict initial status and transitions over time from substance use behavior

LTA with covariates Can have… One or more predictors of Time 1 latent status membership One or more predictors of transition probabilities

Logistic regression A baseline-category logit model is the default for predicting Time 1 latent status and transitions over time Must specify reference group If 5 classes/statuses, you get 4 odds ratios Non-daters (reference) Daters Monog- amous Multi-part Safe Exposed .19 .29 .12 .23 .18

Effect of substance use at Time 1 Past-year cigarette use 43% yes Past-year drunkenness 24% yes Past-year marijuana use 28% yes Non-daters specified as reference group for baseline-category logit model

Effect of substance use at Time 1 Overall tests of significance Cigarette use: Change in 2logL (4 df) = 82.5 p<.0001 Drunkenness: Change in 2logL (4 df) = 81.0 Marijuana use: Change in 2logL (4 df) = 158.0

Effect of substance use at Time 1 Latent Status Cig. Use Drunk Mar. Use Non-daters --- Daters 2.0 3.4 1.7 Monogamous 2.8 3.7 2.5 Multi-partner safe 3.5 2.6 Multi-partner exposed 3.2 8.4 10.5 Adolescents who report marijuana use are 10.5 times more likely to be in the Multi-partner exposed latent status at Time 1 (relative to the Non-daters) than adolescents who report no marijuana use. (Risk of membership in Multi-partner exposed status relative to Non-daters status is 10.5 times greater for those who report marijuana use)

Effect on transitions --- 0.9 1.6 1.1 3.6 0.6 2.0 3.0 1.0 1.0+ 1.0* Non-daters Daters Mono-gamous Multi-part Safe Multi-part Exposed --- 0.9 1.6 1.1 3.6 0.6 2.0 3.0 1.0 1.0+ Multi-part Safe 1.0* Exposed 1.3 0.7 Among non-daters at time 1, adolescents who reported drunkenness at time 1 were 3.6 times more likely to transition to multi-partner exposed at time 2 relative to staying non-daters at time 2, compared to adolescents who did not report drunkenness at time 1. *Logit model skipped for this row of transition probability matrix +Parameter fixed to zero (status not included in logit model)

Conclusions about effects of SU Drunkenness and marijuana use predict membership in the Multi-Partner Exposed latent status more strongly than cigarette use Drunkenness is a stronger predictor of transitioning to high- risk sexual behavior among adolescents in the Non-daters and Daters latent statuses at Time 1, compared to adolescents in the Monogamous and Multi-Partner Safe latent statuses

Additional research questions Possible covariates might include… Temperament Academic achievement Age Income-to-needs

Additional research questions Example research questions: Does child temperament predict dating and sexual risk behavior statuses at Time 1? What is the increase in odds of membership in the high-risk status (relative to the ‘Non-daters’ status) corresponding to a one-unit change in academic achievement? How does age relate to the probability of transitioning from ‘Monogamous’ to ‘Multi-Partner Exposed’

THANK YOU!! Bethany C. Bray bcbray@psu.edu methodology.psu.edu bethanycbray.wordpress.com