Multivariate Multilevel Models Getachew A. Dagne George W. Howe C. Hendricks Brown Funded by NIMH/NIDA 11/20/2014 (ISSG Seminar) 1
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 2
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.
What are Questions that Lead to New Multilevel Multivariate Models? Example 1: Implementation Research (Adapted from Whole Day 3 rd Generation Trial ongoing study in Baltimore City) 11
Multivariate in the predictor Teacher attentio n Teacher response to aggression Later Drug Abuse Teacher reading aid 12
Multilevel in the predictor Level 1 (Child) Response toward Child 1 Response toward Child 2 Response toward Child 3 Response (C1) Overall Rate of Behavior Child 1 Aggress Teacher response to aggression Level 2 (Classroom) Later Drug Use Response (C2) Response (C3) Child 2 Aggress Child 3 Aggress Impact of Behavior (Slope) 13
Multilevel multivariate in the Mediator Attentio n rate Attentio n Impact Presence or absence of implementation Resp. to aggr rate Resp. to aggr Impact Later Drug Use Reading aid rate Reading aid Impact 14
Example 2: Etiology Research (Couples Level Social Interaction Processes and Mediators of the Effects of Job Loss on Depression) Couples interaction: Rates of behavior and associations between behaviors: Job loss stressors Later Depression 15
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 16
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 Random effects: Unmeasured dyadic level variables related to the frequency counts. 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
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 19
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
Example: Microcoded Discourse Wife: Your idea is good. (Problem Talk) Wife: But I still don t think you really care how I feel about this. (Guilt Husband: That s just like you. (Criticism) Husband: This is your personality again. (Criticism) Husband: You re the type that s always blaming others. (Criticism) Wife: Well if you would do what you say you will, then I wouldn t have t remind you all the time. (Guilt Induction) Time Units B 1 2 3 4 5 6 7 E Wife: W-PT W-GI W-GI W-GI Husband: H-CR H-CR H-CR 22
Current Approaches in Characterizing Interaction B Function f(x) Episode-Level Interaction Structure E Tendency of WGI Frequency counts Association of WGI & HCR Sequence counts Conditional prob. Adjusted residual Log odds ratio Precursors Underlying Process Outcomes Example: Negative reciprocatio n 23
ANTECEDENT TABLE OF SEQUENCE COUNTS CONSEQUENT PSF MALE PSI EMV EMI PSF FEMALE PSI EMV EMI MALE FEMALE PSF PSI EMV EMI PSF PSI EMV EMI SELF-SELF TRANSITION FEMALE-MALE TRANSITION MALE-FEMALE TRANSITION SELF-SELF TRANSITION
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 25
Multilevel Multivariate Models n ijkm is the number of times a pair of behaviors occurred, and n ijkm ~ Poisson (μ ijkm ), where log(μ ijkm ) = θ ijkm + log(n km ) + ε ijkm. θ ijkm = ω + R i α km + C j β km + A ij γ km, α km = α + ζ 1 W k + u 1km, β km = β + ζ 2 W k + u 2km, γ km = γ + ζ 3 W k + u 3km, where W k is a vector of predictor variables, and ζ s are vectors of coefficients indexing 26 the effects of these variables on row (R i ),
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 27
VALENCE ASSOCIATION CONTRAST MATRIX CONSEQUENT 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 28
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) 29
ANTECEDENT Example: Positive valence in both quadrants Positive Climate, Productive Problem Solving CONSEQUENT MALE FEMALE PSF PSI EMV EMI PSF PSI EMV EMI MALE FEMALE PSF PSI EMV EMI PSF PSI EMV EMI 1-1 1-1 0 0 0 0 1-1 1-1 0 0 0 0 1-1 1-1 0 0 0 0 1-1 1-1 0 0 0 0 30
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
Covariances of all random effects i r1 r2 r3 c1 c2 c3 a1 a2 a3 a4 r1 r2 r3 c1 c2 c3 a1 a2 a3 a4 i 32
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. 33
-0.6-0.4-0.2 0.0 0.2 2 Multidimensional scaling method (cont d) r1 a2a4 c1 a1 a3 i r3 c3 r2 c2 34-0.6-0.4-0.2 0.0 0.2 0.4 0.6
Latent Factor Analysis Two approaches 1. Two-step method 2. Level-two method 35
Latent Factor Analysis (cont d) Two-step method: r2 f2 c2 f3 r1 r3 f4 a1 a2 a3 a4 c1 c3 36
Latent Factor Analysis (cont d) Level-two method: 37
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.
Depression 12 14 16 18 20 Gender moderates association for depression Female Male -0.3-0.2-0.1 0.0 0.1 0.2 0.3 Engaged Problem Solving
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
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