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Multivariate Multilevel

Models Getachew A. Dagne

George W. Howe C. Hendricks Brown

Funded by NIMH/NIDA

11/20/2014 (ISSG Seminar)

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Outline

What is Behavioral Social Interaction?

Importance of studying social interaction

Methods of measuring social interactions: Observational Research

Multivariate multilevel modeling

Example: Couples data and Micro-coded behaviors

Results

What is Behavioral Social Interaction?

The most basic unit of all behavior is ACT

Everything we do is an ACT: for example, eating, working, dressing, preparing for class, taking tests … any and all actions involve acts

Some acts have implications for no one else but ourselves

Most involve some relationship to other people which constitutes some form of social interaction.

Social Interaction (cont’d)

Social interaction – the process by which people act and react in relation to others.

This includes any and all social behavior,

including interacting with material

culture (books, papers, street signs, etc.)

independent of communicating with

another human being.

Social Interaction (cont’d)

In social science, a social interaction refers to a relationship between

two (i.e. a dyad),

three (i.e. a triad) or

more individuals (e.g. a social group).

Social Interaction (cont’d)

In general, there are different kind of social interactions :

One-on-one interaction (e.g., normal conversation)

Many-on-one interaction (e.g., influence from many-on-one)

One-on-many interaction (e.g., leadership)

Many-on-many interaction (e.g., demonstration)

Why study social interaction?

The study of social interactions, or social networks, is central to understanding the dynamics of the relations between social actors, as well as their behaviors and performance.

Social skills are learned behavior that allow people to achieve social reinforcement and to avoid social punishment

Deficiency in social skills lead to

emotional and behavioral disorders.

Why study social interaction?

Some disorders that show an impairment in social skills:

Conduct Problems

Mood Disorders

Anxiety Disorders

Attention-Deficit Hyperactivity Disorder (ADHD)

Learning Disabilities

Biostatistical Methods in Social Interaction

Multilevel Multivariate Models?

This talk presents new methods for specifying and modeling theoretically meaningful patterns of interactions in a behavioral sequence.

For a single transition during an interaction, such as the transition from a wife’s action to a husband’s reaction, a univariate multilevel model has been used to characterize contingency strength between any two individual behavior categories.

For analyzing interaction patterns involving transitions to and from both actors, a multivariate multilevel model is proposed.

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What are Questions that Lead to New Multilevel

Multivariate Models?

Example 1: Implementation Research (Adapted from Whole Day 3rd

Generation Trial – ongoing study in Baltimore City)

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Multivariate in the predictor

Teacher attention

Teacher response to aggression

Teacher reading aid

Later Drug Abuse

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Multilevel in the predictor

Teacher response to aggression

Later Drug Use

Response (C1) Child 1 Aggress

Response (C2) Child 2 Aggress

Response (C3) Child 3 Aggress

Impact of Behavior (Slope)

Response toward Child 3

Response toward Child 1

Response toward Child 2

Overall Rate of Behavior

Level 1 (Child)

Level 2 (Classroom)

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Multilevel multivariate in the

Mediator

Later Drug Use

Attention

rate

Attention Impact

Resp. to aggr rate

Resp. to aggr Impact

Reading aid

rate

Reading aid

Impact

Presence or absence of implementation

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Example 2: Etiology Research

(Couples Level Social Interaction Processes and

Mediators of the Effects of Job Loss on Depression)

Later Depression

Couples interaction: Rates of behavior and associations between behaviors:

Job loss stressors

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Using Couple-Level Data as

Multilevel Mediators

Couples interaction:

Rates of behavior of female partner and male partner

Associations between antecedent behaviors and consequent behaviors of couples – Impact of Husband Behavior on Wife Behavior

– Impact of Wife Behavior on Husband Behavior

Example of Research Question: If husbands interrupt their wives

are wives more likely later to interrupt their husbands?

What is Multivariate Multilevel Modeling?

Modeling individual growth and growth of clusters, what factors affect growth of clusters?

Multivariate Growth Mixture Models (MGMM) – patterns of growth for individuals and clusters.

Example of Multilevel Multivariate

Modeling

Multilevel: Level 1: Frequency Counts of husband

and wife behavioral sequences collapsed over time

Level 2: Dyads -- predictors and responses.

Multivariate: Two groups of behavioral

sequences: Wife->Husband and Husband->Wife

Random effects: Unmeasured dyadic level variables related to the frequency counts. Random effects serve as mediators of

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Observational Research

Direct observation is a powerful method for studying human interactions that form both risk and protective mechanisms involved in the development and maintenance of psychopathology and substance use. Parent-child

Peer-peer

Spouse-spouse

Couples’ Data (Howe, 1995)

The proposed method is illustrated through

analyzing a dataset from 254 couples experiencing substantial stress occasioned by loss of employment.

Ethnicity: 54% European-American, 46% African-American

Education: Not completed H.S. (10%), H.S completed (27.9%), some college (45.1%), postgraduate (16.8%)

Income: median family income (40k - 44k)

BEHAVIOR CATEGORIES

Problem-Solving Facilitation (PSF) – Propose positive solution

– Accept responsibility

Problem-Solving Inhibition (PSI) – Problem denial

– Propose negative solution

Emotional Validation (EMV) – Summarize other

– Primary support

Emotional Invalidation (EMI) – Personal criticism

– Guilt induction

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Example: Microcoded Discourse

Wife: But I still don’t think you really care how I feel about this. (Guilt Induction)

W-GI

Husband: That’s just like you. (Criticism)

H-CR

Husband: This is your personality again. (Criticism)

H-CR

Husband: You’re the type that’s always blaming others. (Criticism)

H-CR

Wife: Well if you would do what you say you will, then I wouldn’t have to remind you all the time. (Guilt Induction)

W-GI W-GI

E

Wife: Your idea is good. (Problem Talk)

W-PT

B

Wife:

Husband:

Time Units

1 2 3 4 5 6 7

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Current Approaches in

Characterizing Interaction B E

Episode-Level Interaction Structure

Function f(x)

Precursors Outcomes

Tendency of WGI Frequency counts

Association of WGI & HCR Sequence counts Conditional prob.

Adjusted residual Log odds ratio

Underlying Process

Example: Negative reciprocation

TABLE OF SEQUENCE COUNTS

MALE FEMALE

PSF PSI EMV EMI PSF PSI EMV EMI

PSF

MALE PSI

EMV

EMI

PSF

FEMALE PSI

EMV

EMI

AN

TECED

EN

T

CONSEQUENT

SELF-SELF

TRANSITION

SELF-SELF

TRANSITION

FEMALE-MALE TRANSITION

MALE-FEMALE TRANSITION

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Sources of Variation

In a couple interaction, there are three sources of variation we would like to capture:

1. Actor (Wife)

2. Partner (Husband)

3. Actor-Partner Interaction

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Multilevel Multivariate Models

nijkm is the number of times a pair of behaviors occurred, and nijkm ~ Poisson (μijkm), where

log(μijkm) = θijkm + log(nkm) + εijkm. θijkm = ω + Riαkm + Cjβkm + Aij γkm, αkm = α + ζ1 Wk + u1km, βkm = β + ζ2 Wk + u2km, γkm = γ + ζ3 Wk + u3km, where Wk is a vector of predictor variables,

and ζ’s are vectors of coefficients indexing the effects of these variables on row (Ri ), column (Cj), and association (Aij ) effects.

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Simplifying the Association

Structure ?

9 random effects for association

9 means of these random effects

9 variances of these random effects

36 covariances among themselves

84 covariances with other random effects

Are there simple associations that have both theoretical interest and are important empirically?

Valence, Positive and Negative Valence

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VALENCE

ASSOCIATION CONTRAST MATRIX

MALE

PSF PSI EMV EMI

PSF 1 -1 1 -1

FEMALE PSI -1 1 -1 1

EMV 1 -1 1 -1

EMI -1 1 -1 1

CONSEQUENT

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Association Parameters

Valence could be further divided into two parts based on substantive consideration as

(1) Positive Valence: Contrasts with positive antecedent behaviors (e.g., problem solving facilitation, and emotional validation)

(2) Negative valence: Contrasts with negative antecedent behaviors (e.g., problem solving inhibition, and emotional invalidation)

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Example: Positive valence in

both quadrants

MALE FEMALE

PSF PSI EMV EMI PSF PSI EMV EMI

PSF

MALE PSI

EMV

EMI

PSF

FEMALE PSI

EMV

EMI

AN

TE

CE

DE

NT

CONSEQUENT

1 1

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1 1

11

-1 -1

-1-1

-1 -1

-1-1

0 0 0 0

0 0 0 0

0 0 0 0

0 0 0 0

Positive Climate, Productive Problem Solving

Modeling two quadrants simultaneously

We model processes that involve both H->W and W->H transitions.

Associations: a1 = positive valence for husband to wife transition a2 = negative valence for husband to wife transition a3 = positive valence for wife to husband transition a4 = negative valence for wife to husband transition

Marginals: Within-quadrant marginals are almost identical across the

two quadrants, so we chose to model just one set of marginals.

Row marginal random effects: r1-r3 Column marginal random effects: c1-c3

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Covariances of all random effects

r1 r2 r3 c1 c2 c3 a1 a2 a3 a4 i

r1 r2 r3 c1 c2 c3 a1 a2 a3 a4 i

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Multidimensional scaling method

Multidimensional scaling is an exploratory method which we use to help us visualize proximities of covariances of random effects in a low dimensional space.

This allows us to gain insight in the underlying structure of relations between marginal and association random effects by providing a geometrical representation of these relations.

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Multidimensional scaling method

(cont’d)

1

2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-0

.6-0

.4-0

.20

.00

.2

r1

r2

r3

c1

c2

c3a1

a2

a3

a4

i

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Latent Factor Analysis

Two approaches

1. Two-step method

2. Level-two method

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Latent Factor Analysis (cont’d)

Two-step method:

f2 c2

r2

r1

r3

c1

c3 a1

a2

a3

a4

f3

f4

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Latent Factor Analysis (cont’d)

Level-two method:

Latent class and latent factor model for these

10 random effects

Y1 Y2 Y31 Y32

r1 r2 a3

a4

Latent Factor

A two-factor solution appeared to provide the most parsimonious characterization of the data:

A factor composed of four positive behavior rates (male PSF(r1), male EMV(r3), female PSF(c1), female EMV(c3)), named as engaged problem solving

The second factor was composed of the four association effects (male positive valence(a1), male negative valence(a2), female positive valence(a3), female negative valence(a4)), named as total valence

Problem-Solving Interaction and

Relationship Quality 1. It was found that engaged problem

solving was strongly related to perceptions of dyadic adjustment

marital expectations

blame attributions

2. Total valence was not significantly associated with any of the three relationship quality outcomes.

Gender moderates association

for depression

Engaged Problem Solving

Dep

ress

ion

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

1214

1618

20

FemaleMale

Interpretations

Engaged problem solving was strongly associated with depression, and this association was moderated by gender, indicating that higher levels of engaged problem solving were associated with lower levels of depression.

The association between total valence and anger/irritability was significantly moderated by role, indicating that higher levels of total valencewere associated with

lower anger/irritability for job seekers .

References

Dagne, G. A., Howe, G. W., Brown, C. H., & Muthen, B. O. (2002)

Hierarchical modeling of sequential behavioral data: An empirical Bayesian approach. Psychological Methods, 7, 262-280

Dagne, G. A., Brown, C. H., & Howe, G. W. (2003). Bayesian

hierarchical modeling of heterogeneity in multiple contingency tables: An application to behavioral observation data. Journal of Educational & Behavioral Statistics, 28, 339-352.

Howe, G.W., Dagne, G. A., & Brown, C. H. (2005). Multilevel

methods for modeling observed sequences of family interaction. Journal of Family Psychology, 19, 72-85.

Dagne, G. A., Brown, C. H. , & Howe, G. W. (2007) Hierarchical modeling of sequential behavioral data: Examining complex association patterns in mediation models. Psychological Methods

12, 298-316