Trang Quynh Nguyen May 9 2016 41068601 Advanced Quantitative Methods in the Social and Behavioral Sciences A Practical Introduction Objectives Provide a QUICK introduction to latent class models and finite mixture modeling with examples ID: 721327
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Slide1
A quick intro to latent class and finite mixture modeling
Trang Quynh Nguyen, May 9, 2016
410.686.01 Advanced Quantitative Methods in the Social and Behavioral Sciences: A Practical IntroductionSlide2
Objectives
Provide a QUICK introduction to latent class models and finite mixture modeling, with examples
What is possible for your research
Refer to relevant courses in JHSPH
How to implement some common models
Alert to literature on these methods
Methodological developments
A partial hands-on exercise at latent class analysis
A tangible feel, if we have enough timeSlide3
Overview
Latent variable measurement
Recall
factor
analysis
Latent class analysis (LCA)
Types of latent variable measurement models
LCA-based structural models
Latent class regression – LC
with
predictors (LCR)
Latent class with
(distal)
outcome (LCD)
Latent transition model
Mixture modeling
Mixture of distributions
Cross-sectional mixture models
Longitudinal mixture models
Hybrid/complicated modelsSlide4
Overview
Latent variable measurement
Recall factor analysis
Latent class analysis (LCA)
Types of latent variable measurement models
LCA-based structural models
Latent class regression – LC with predictors (LCR)
Latent class with distal outcome (LCD)
Latent transition model
Mixture modeling
Mixture of distributions
Cross-sectional mixture models
Longitudinal mixture models
Hybrid/complicated modelsSlide5
Latent factor model (CFA)
Latent factor = latent (unobserved) continuous variable
Usually refers to a construct that cannot be measured directly (e.g., happiness, optimism, depression, anxiety)
but is measured indirectly, usually using a multi-item scale.
The scale items reflect the latent construct, i.e., the levels of the items are influenced by the level of the latent construct.Slide6
depression
sad
lose interest in things
t
hink of death
Ex.: Depression scale (PHQ-9)
eating problems
sleeping problems
psychomotor symptoms
feeling bad about self
trouble concentrating
fatique
Latent factor model (CFA)Slide7
Latent factor
model (CFA)
. . .
continuous
. . .
’s are called loadings.
with continuous
’s
Psychosocial statistics 1Slide8
A similar idea: LATENT CLASS MODEL
. . .
categorical
How may this be useful?
When would you want to use it?
The difference is: the latent variable is categorical.Slide9
. . .
categorical
Data reduction
T
he idea of subgroups/subtypes
/mixture of distributions
LATENT
CLASS MODELSlide10
. . .
. . .
with binary
’s
.
’s are class prevalences;
’s are conditional
probabilities.
Psychosocial statistics 1
LATENT
CLASS MODELSlide11
f
amily negativity
BEATUP
LCA ex. 1: negative family treatment of SMW
INSULT
LOCKUP
DOCTOR
SHAMAN
MONITOR
DISOWN
SUICMON
ASKOTHER
CUTSUPP
m
y dissertation paper 1Slide12
m
y dissertation paper 1Slide13
LCA ex. 2: risk-for-substance use subgroups
Figure 1 from: Lanza
, S. T., & Rhoades, B. L. (2013). Latent class analysis:
An
alternative perspective on subgroup analysis in prevention and treatment.
Prevention Science
,
14
(2), 157–68
.Slide14
LCA ex. 3: drug use subtypes
Based on Table 2.2 in S. Janet Kuramoto’s dissertationSlide15
Latent
variable
Observed indicators
Type of analysis
continuous
continuous
Factor
Analysis
continuous
binary/ordinal
Latent Trait
Analysis
/Factor Analysis
continuouscountFactor Analysis
categoricalcategorical
Latent Class Analysiscategorical
continuousLatent Profile Analysis
Types of latent variable measurement modelsSlide16
Overview
Latent variable measurement
Recall factor model
Latent class model (LCA)
Types of latent variable measurement models
LCA-based structural models
Latent class regression – LC with predictors (LCR)
Latent class with distal outcome (LCD)
Latent transition model (LTA)
Mixture modeling
Mixture of distributions
Cross-sectional mixture models
Longitudinal mixture models
Hybrid/complicated modelsSlide17
LATENT CLASS REGRESSION
X -> C:
In LCA, we had class prevalence:
Now we have:
. . .
Psychosocial statistics 2Slide18
X -> C:
In LCA, we had class prevalence:
Now we have:
. . .
What regression model can be used to estimate
?
Slide19
C has 2 categories: logistic regression
C has 3+ categories: multinomial logistic regression
. . .
Slide20
2-category C: review logistic regression
Model using X to predict C:
Interpretation:
odds ratio
Condiser
binary X: 0=rural,
1=urban. Slide21
2-category C: review logistic regression
Predicting conditional probabilities (conditional class prevalence):
Slide22
3-category C: multinomial logistic regression
Model:
Interpretation:
partial odds ratio
BIO 624
(or
ratio of risk ratios
)
Slide23
LCR ex.: partial odds ratios, adjustedSlide24
3-category C: multinomial logistic regression
Predicting conditional probabilities (conditional class prevalence):
Slide25
LCR: how to implement
1-step method (simultaneously estimate measurement and structural components): Psychosocial Statistics 2
3-step methods: look up literatureSlide26
LATENT CLASS WITH DISTAL OUTCOME
m
y dissertation paper 2Slide27
LATENT TRANSITION ANALYSIS
Slide28
P(t2 status | t1 status)
Time 2
Non-users
Cigarette smokers
Binge drinkers
Bingers with marijuana use
Non-users
0.895
0.042
0.062
0.002
Time 1
Cigarette smokers
0.165
0.645
0.002
0.188
Binge drinkers
0.115
0.000
0.827
0.058
Bingers with marijuana use
0.062
0.000
0.000
0.938
LTA ex. 1: latent transition probabilities
Part of Table 4 from Lanza
, S. T., Patrick, M. E., & Maggs, J. L. (2010). Latent Transition Analysis: Benefits of a Latent Variable Approach to Modeling Transitions in Substance Use.
Journal of Drug Issues
,
40
(1), 93–120
.Slide29
LTA ex. 2: latent transition analysis with covariates
Figure 1 from: Chung
, H., Park, Y., & Lanza, S. T. (2005). Latent transition analysis with covariates: pubertal timing and substance use behaviours in adolescent females.
Statistics in Medicine
,
24
(18), 2895–910
.
C1 = puberty status
No puberty
Mid-puberty
Puberty
C2 = substance use
No use
AlcoholCigarettes
Alcohol + cigarettesAlcohol + cigarettes + drunkSlide30
Overview
Latent variable measurement
Recall factor model
Latent class model (LCA)
Types of latent variable measurement models
LCA-based structural models
Latent class regression – LC with predictors (LCR)
Latent class with distal outcome (LCD)
Latent transition model (LTA)
Mixture modeling
Mixture of distributions
Cross-sectional mixture models
Longitudinal mixture modelsHybrid/complicated modelsSlide31
Mixture of distributions
A single continuous random variable
Example: heightSlide32
Male height world map (unknown source)Slide33
p
op 314 m
p
op 9.5 m
p
op 89 mSlide34Slide35Slide36Slide37Slide38Slide39
Mixture of distributions
Multivariate binarySlide40Slide41
Cross-sectional mixture models
Latent class analysis (LCA)
Latent profile analysis (LPA)
Latent transition analysis (LTA) with cross-sectional data
Ex. Puberty classes predicting substance use classes (concurrent time)Slide42
Longitudinal mixture models
Repeated measures LCA
Latent transition analysis (LTA) with longitudinal data
Ex. Substance use status at time 1 predicting substance use status at time 2
Growth mixture modelsSlide43
Growth mixture (simulated data)Slide44
Non-mixture growth model
one average curve for all
1
1
1
1
1
2
3
Think regression:
What is different?
correlation among
LDA classSlide45
Non-mixture growth model
each person j, their own curve
1
1
1
1
1
2
3
Random effects model:
LDA classSlide46
If relationship with time is non-linear…
1
1
1
1
1
2
3
Think regression:
1
4
9Slide47
Growth mixture model
1
1
1
1
1
2
3
1
4
9
Psychosocial statistics 2Slide48
Ex1. linear modelSlide49
Ex2. Trajectories of marijuana use:
quadratic logistic model
Figures from: Juon
, H.-S., Fothergill, K. E., Green, K. M., Doherty, E. E., & Ensminger, M. E. (2011). Antecedents and consequences of marijuana use trajectories over the life course in an African American population.
Drug and Alcohol Dependence
,
118
(2-3), 216–23
.Slide50
An example of hybrid/more complex model
Muthén, B. O., & Masyn, K. E. (2005). Discrete-time survival mixture analysis.
Journal of Educational and Behavioral Statistics
,
30
(1), 27–58
.Slide51
Overview
Latent variable measurement
Recall factor model
Latent class model (LCA)
Types of latent variable measurement models
LCA-based structural models
Latent class regression – LC with predictors (LCR)
Latent class with distal outcome (LCD)
Latent transition model (LTA)
Mixture modeling
Mixture of distributions
Cross-sectional mixture modelsLongitudinal mixture models
Hybrid/complicated modelsSlide52
Objectives
Provide a QUICK introduction to latent class models and finite mixture modeling
What is possible for your research
Refer to relevant courses in JHSPH
How to implement some common models
Alert to literature on these methods
Methodological advancements for better analysis
A partial hands-on exercise at latent class analysis
A tangible feel, if we have enough timeSlide53