cutting-edge advances in lca for today’s behavioral scientists

cutting-edge advances in lca for today’s behavioral scientistsBETHANY C. BRAY

THE METHODOLOGY CENTER, PENN STATE



Grr! Arg! What is she doing?

U! There’s a u!



Grr! Arg! What is she doing?

U! There’s a u!

cutting-edge advances in lca for today’s behaviouralscientistsBETHANY C. BRAY


outline of today’s talkmotivation

lca with a distal outcome

causal inference with lca

motivation

motivation

so, I heard a rumor…

motivation

so, I heard a rumor…

there’s nothing new left to do in lca?

role of lca is growinglatent class analysis (LCA) increasingly used to identify subgroups of individuals based on unique patterns of…◦ behavior

◦ risk exposure

◦ mental health symptoms

◦ other characteristics

role of lca is growingit’s a powerful, intuitive tool for studying population heterogeneity

but, what is LCA?subgroups (i.e., classes) are comprised of individuals who are similar in their responses to a set of observed variables

true class membership is unknown; we infer it from responses to a set of observed variables

an example: risk exposure classesLanza & Rhoades, 2012, Prevention Science

risk

profiles

household

poverty

peer

alcohol use

neighbor-

hood

poverty

…

complex new questionsnew methods are needed to address the next generation of complex questions involving latent class variables

does risk exposure class moderate effect of X on Y?

does substance use norms class mediate effect of X on Y?

complex new questionsessential first step:

how is latent class membership linked to later outcomes?

e.g., how is childhood risk profile membership associated with adolescent binge drinking?

neighbor-

hood

poverty

predicting an outcome

binge

drinking

1) low risk

2) peer risk

3) economic risk

4) household + peer risk

5) multilevel risk

risk

profiles

household

poverty

peer

alcohol use…

lca with a distal outcome

the challengethe mathematical model for predicting latent class membership from a covariate is well-understood

estimating the association between a latent class predictor and distal outcome presents a difficult methodological problem

traditional approacheshistorically, classify-analyze approaches have been used to solve the problem,

which rely on posterior probabilities◦ each individual has probability of membership in each

latent class: P(C|U)

traditional approachesposterior probabilities form the basis for classify-analyze approaches

◦ classification step:assign individuals to classes based on probabilities

◦ analysis step:treat class membership as known in analysis model

modal assignmentselect optimal latent class model

calculate posterior probabilities for each individual

assign individuals to latent class with max post prob

conduct outcome analysis

multiple pseudo-class drawsselect optimal latent class model

calculate posterior probabilities for each individual

assign individuals based on distn of post probs

conduct outcome analysis

repeat steps 3 & 4 multiple times

combine results using rules from multiple imputation

do these approaches work?the outcome analysis gives us Y|C◦proportion engaging in BINGE DRINKING given latent class

however, these approaches can severely attenuate estimated CY path

substantial attenuation

Cohen’sEffect Size True P(Binge)

Bias forPseudo-class (Traditional)

Large (.5) .67 -.19

Medium (.3) .48 -.10

Small (.1) .37 -.04

No effect .30 .000

contemporary approachesthree new approaches work well under certain conditions◦ many recently published simulation studies

however, no comprehensive overview summarizing the approaches and their assumptions, or integration of “take-home messages” across simulation studies

weighting by classification errorproposed in multiple papers by collaborators of Hagenaars and Vermunt since 2004

colloquially known as the “BCH approach”

adjusts outcome analysis by classification error of posterior probability-based assignments

Bakk, Z., & Vermunt, J. K. (2016). Robustness of stepwise latent class modeling with continuous distal outcomes. Structural Equation Modeling, 23, 20-31.

weighting by classification errorassign individuals to classes based on responses to indicators only

save classification error rate for each class

treat assignments as known in subsequent analysis model weighted by the classification error rates

Bayes’ theorem based approachuses Bayes’ theorem to produce distribution of Ygiven C using distribution of C given Y

colloquially known as the “LTB approach”

Lanza, S. T., Tan, X., & Bray, B. C. (2013). Latent class analysis with distal outcomes: A flexible model-based approach. Structural Equation Modeling, 20, 1-26.

Bayes’ theorem based approachfit latent class model, include distal outcome as covariate

use Bayes’ theorem to reverse the direction of effect, empirically derive distribution of the distal outcome given class membership

)(

)()|()|(

Cf

YfYCfCYf

inclusive classify-analyzegoal is to improve posterior probabilities

Based on ideas from multiple imputation (of missing data)

Bray, B. C., Lanza. S. T., & Tan, X. (2015). Eliminating bias in classify-analyze approaches for latent class analysis. Structural Equation Modeling, 22, 1-11.

inclusive classify-analyzeassign individuals to classes based on responses to indicators and distal outcome◦ assignment typically uses modal assignment or multiple

pseudo-class draws

then, treat assignments as known in a subsequent analysis model

reduced attenuation

Cohen’sEffect Size

True P(Binge)

Pseudo-class (Traditional)

Pseudo-class(Inclusive)

Large (.5) .67 -.19 .001

Medium (.3) .48 -.10 .006

Small (.1) .37 -.04 .001

No effect .30 .000 .000

Approach Low Risk Peer RiskEconomic

RiskH.Hold & Peer Risk

MultilevelRisk

Pseudo-class(Traditional) .16 .37 .17 .39 .41

Pseudo-class (Inclusive) .11 .41 .12 .62 .36

in real life?

the goodall contemporary approaches substantially reduce attenuation and can result in unbiased estimates

software of some kind is available for all contemporary approaches◦Latent Gold

◦Mplus

◦SAS

the badno single software package can do all approaches with all types of outcomes

some approaches are sensitive to violations of model assumptions

standard errors need work◦ but, bootstrapping seems

promising

APPROACH

Reducesbias

High-quality

standard errors

Canimplement in any LCA software

Measure-mentmodelstable across

analyses

Does not require

assigning individual

Robust to violations of assum-

ptions

Unlimited model

complex-ity

Traditional No No No

Weighting MaybeNo

Latent Gold + Mplus

No Probably Maybe

Bayes Binary

outcomeNo

SAS + MplusSometimes

Nobut can be improved

No

Inclusive No Sometimes NoNo

but can be improved

the ugly!

take-home messages1. weighting by classification error emerging as optimal approach

2. active area of research with challenges aheadunderstand assumptions of each approach

obtain high-quality standard errors

what next?let‘s assume we know how to do covariates and outcomes…

how do we handle variables that statistically confound X Cand CY?

causal inference with lca

why are we interested?how do we start thinking about latent class variables as integral components of complex developmental models?

modern approaches to LCA with covariates and distal outcomes estimate correlational associations

can we do better when we have confounding?

druguse

alcohol tobacco other…

druguse


college

standard approachLCA with covariates

logistic regression coefficients represent the correlational association

attending college corresponds to a change in the log-odds of class membership

standard approachbut, in the absence of randomization…

there are many reasons why attending college may appear to be linked to later drug use

these reasons are called selection effects or confounders

druguse


college

confounderse.g., gender, race, income

do we have any solutions?we need modern causal inference methods

instrumental variables

principal stratification

estimating equations

propensity scores





propensity scores

step-by-step1. obtain propensity scores for the exposure

2. calculate inverse propensity weights

3. regress latent class membership on exposure and apply weights

see: Lanza, Coffman, & Xu, 2013; Lanza, Schuler, & Bray, in press

druguse


college


Step 1: obtain propensity scores for attending college

Step 2: Calculate inverse propensity weights

Step 3: regress drug use on college attendance and apply the weights

Pr( 1| ) i i ix confounders




different causal questions areanswered with different weights

upweight under-represented individuals; downweight over-represented ones

druguse


college





okay, but what about with a distal outcome?

druguse


depression

standard approachum, not yet, but we have a lot of options

regardless, effects represent correlational associations

class membership corresponds to a particular probability of later having depression

standard approachbut, again, in the absence of randomization…

there are many reasons why drug use class membership may appear to be linked to later depression

druguse


depression






propensity scores





propensity scores

latent class causal analysisestimating equations: latent class causal analysis (LCCA)

conceptually, combines…LCA with confounders included as covariatesregression of the outcome on the confounders

…in order to produce all potential outcomes and directly calculate effects

see: Coffman, Bray, Dziak, Liu, & Lanza, under revision; Schafer & Kang, 2010

latent class causal analysisthis approach is implemented in the R package lcca

see: Schafer & Kang, 2013

practical limitations todaymodel identification

software capabilities

technical support

an attractive alternative?weighting by classification and inverse propensity weights or weighting with inclusive classify-analyze…

are these options here?

an attractive alternative?initial investigations using the Add Health data are promising for both binary and continuous outcomes for weighting by classification error…

final thoughts

although causal inference methods are becoming more common, there are a number of issues to resolve with latent outcomes and latent exposures

propensity scores provide a straightforward tool for estimating effects, but they are not the only tool available

the goal, of course, is to be able to model something like the following scenario…

druguse

alcohol tobacco substanceJ…

druguse


intervention

druguse


interventionnorms

druguse


interventionnorms

family

peers

druguse


interventionnorms

gender

family

peers

druguse


interventionnorms

gender

family

peersaddiction

druguse


interventionnorms

gender

family

peersaddiction

confounders

collaborators: it takes a village!

John

Dziak

Stephanie

Lanza

Michael

Russell

Jie-Ting

Zhang

Xianming

Tan

StephanieLanza


DonnaCoffman

NicoleButera

DanielAlmirall

XiaoyuLiu

John Dziak


MeganSchuler

ShuXu

acknowledgmentsfunding from NIH

The project described was supported by award numbers P50-DA010075 and P50-DA039839 from the National Institute on Drug Abuse (NIDA) and R21-DK082858 from the National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK). The content is solely the responsibility of the authors and does not necessarily represent the official views of NIDA, NIDDK, or the National Institutes of Health (NIH).

data from UNC (Add Health)The project described used data from Add Health, a program project directed by Kathleen Mullan Harris and designed by J. Richard Udry, Peter S. Bearman, and Kathleen Mullan Harris at the University of North Carolina at Chapel Hill, and funded by grant P01-HD31921 from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, with cooperative funding from 23 other federal agencies and foundations. Special acknowledgment is due Ronald R. Rindfuss and Barbara Entwisle for assistance in the original design. Information on how to obtain the Add Health data files is available on the Add Health website (www.cpc.unc.edu/addhealth). No direct support was received from grant P01-HD31921 for this analysis.

http://www.cpc.unc.edu/addhealth

thank you!Bethany C. Bray, Ph.D.◦ Research Associate Professor,

College of Health and Human Development

◦ Associate Director, The Methodology Center

◦ Associate Training Director, Prevention and Methodology Training Program

[email protected]

bethanycbray.wordpress.com

methodology.psu.edu/people/bbray

The Methodology Center404 HHD Bldg.University Park, PA 16802

[email protected]

methodology.psu.edu

mailto:[email protected]

http://bethanycbray.wordpress.com/

http://methodology.psu.edu/people/bbray

mailto:[email protected]

http://methodology.psu.edu/

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cutting-edge advances in lca for today’s behavioral scientists