CLOCgonzalez

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Published on January 15, 2008

Author: Berta

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Modeling Interdependence: Toward a General Framework:  Modeling Interdependence: Toward a General Framework Richard Gonzalez, U of Michigan Dale Griffin, U of British Columbia Slide2:  The Nested Individual Underlying Premises:  Underlying Premises Nonindependence provides useful information is not a nuisance is a critical component in the study of interpersonal behavior but may not be required in all analyses Historical Analysis:  Historical Analysis Explanatory priority placed on the group Meade-- individual in context of group Durkheim Comte—family as primary social unit Explanatory priority placed on the individual Allport--individual is primary (“babble of tongues”) Necessary Conditions:  Necessary Conditions Homogeneity: similarity in thoughts, behavior or affect of interacting individuals E.g., group-level, emergent processes, norms, cohesiveness Interdependence: individuals influencing each other E.g., actor-partner effects McDougall, 1920, p. 23:  McDougall, 1920, p. 23 The essential conditions of a collective mental action are, then, a common object of mental activity, a common mode of feeling in regard to it, and some degree of reciprocal influence between the members of the group. Statistical Framework Should Mimic Theoretical Framework:  Statistical Framework Should Mimic Theoretical Framework Make concepts concrete Avoid Allport’s “babble” critique Make the model easy to implement TODAY’s Talk One time point; dyads Two or three variables Normally distributed data; additive models Menu of Techniques:  Menu of Techniques Repeated measures ANOVA Intraclass correlation Hierarchical linear models (HLM) Structural equations models (SEM) Common Beliefs about Interdependence in Dyadic Data:  Common Beliefs about Interdependence in Dyadic Data If you don’t correct for interdependence, your Type I errors will be inflated If you don’t correct for interdependence, your results will be ambiguous An HLM program will eliminate all nonindependence problems If you have dyadic data, you must run HLM (or else your paper won’t be published) Slide11:  These beliefs miss what we believe to be the fundamental issue: There is useful psychological information lurking in the “nonindependence” Interdependence is the “very stuff” of relationships. Dyadic Designs: Three Major Categories:  Dyadic Designs: Three Major Categories Subjects nested within groups Exchangeable (e.g., same sex siblings) Distinguishable (e.g., different sex siblings, mother-child interaction) Mixed exch & dist (e.g., same sex & different sex dyads in same design) Univariate versus multivariate Homogeneity versus interdependence Intraclass Correlation: Building Block:  Intraclass Correlation: Building Block Structural Univariate Models: Exchangeable Distinguishable ANOVA Intraclass (& REML) Dyads:  ANOVA Intraclass (& REML) Dyads Intraclass Correlation: HLM Language:  Intraclass Correlation: HLM Language Two level model: Intraclass correlation is given by Pairwise Coding:  Pairwise Coding The Pearson corr of X and X’ is the ML estimator of the intraclass correlation. Pairwise Intraclass Correlation:  Pairwise Intraclass Correlation Example: Personal Victimization Ceballo et al, 2001:  Example: Personal Victimization Ceballo et al, 2001 Pairwise Intraclass (ML): Dyads:  Pairwise Intraclass (ML): Dyads Interdependence:  Interdependence The degree to which one individual influences another Need not be face to face We have a good time together, even when we’re not together (Yogi Berra) Pairwise Generalization:  Pairwise Generalization Predictor X represents the actor’s influence on actor’s Y Predictor X’ represents the partner’s influence on actor’s Y Predictor XX’ represents the mutual influence of both on actor’s Y Example (Stinson & Ickes, 1992):  Example (Stinson & Ickes, 1992) ActorS = ActorV + PartnerV Strangers: an effect of the partner’s verb frequency on the actor’s laughter (in ordinal language, the more my partner talks, the more I smile/laugh) Friends: an effect of the actor’s verb frequency on the actor’s laughter (the more I talk, the more I smile/laugh) Some formulae:  Some formulae Actor regression coefficient V(Actor reg coeff) Partner coef replaces Y with Y’ Interdependence Example:  Interdependence Example Mother and child witness victimization (WV) related to each individual’s fear of crime (FC). Does child’s WV predict child’s FC? Does mother’s WV predict child’s FC? etc Slide31:  Xm Ym Xc Yc a b c d rx r Slide32:  Xm Ym Xc Yc -.1 .2 .3 Not on Welfare Slide33:  Xm Ym Xc Yc .09 .1 Welfare Simple Actor-Partner Model: Pre-post death of spouse:  Simple Actor-Partner Model: Pre-post death of spouse No interdependence problem on the dependent variable Slide35:  Xm Ym Xc Yc a b c d rx r Return to Original Model: Special Case Set a=d and b=d Slide36:  X Y Xm Xc Ym Yc Exm Exc Eym Eyc rd ri ri Latent Variable Model:  Latent Variable Model ri = individual level correlation rd = dyad level correlation The square root of intraclass correlations are the paths Using Path Analysis Rules:  Using Path Analysis Rules Two equations in two unknowns; reason why rxy may be uninterpretable Slide39:  Solving those two equations…. Slide40:  X Y Xm Xc Ym Yc Exm Exc Eym Eyc -.8 .4 .4 .45 .45 .47 .47 Not on Welfare Slide41:  X Y Xm Xc Ym Yc Exm Exc Eym Eyc 1.6 .3 .3 .2 .2 Welfare: latent variable model doesn’t hold What does the correlation of two dyads means?:  What does the correlation of two dyads means? So, there are multiple components to the correlation of dyad means making it uninterpretable…. Multivariate Model: HLM Lingo:  Multivariate Model: HLM Lingo Three-level model: one level for each variable, one level for individual effect, and one level for group effect Difference scores:  Difference scores Frequently, a question of similarity (or congruence) comes up in dyadic research Diff of husband and wife salary as a predictor of wife’s relationship satisfaction Diff of husband and wife self-esteem as a predictor of husband’s coping Difference Scores:  Difference Scores Correlations with difference scores can show various patterns depending on their component correlations The numerator is a weighted sum of the correlations: (rX1Y SX1 – rX2YSX2)Sy Toy Examples One variable is a constant One variable is random “Solutions” :  “Solutions” One can use multiple regression, entering the two variables as two predictors (rather than one difference score). Y = 0 + 1X1 + 2 X2 Problem: doesn’t test specific hypotheses such as “similar is better” or “self-enhancing is better” Model-Based Approach:  Model-Based Approach Questions Discrepancy model (woman’s sat is greatest the more she earns, the less her husband earns) Similarity model (woman’s sat is greatest the smaller the absolute diff in salary) Superiority model (woman’s sat is greatest when she earns more than her husband) Model-Based Approach:  Model-Based Approach Run separate regressions for subjects below and above the “equality line” (or use dummy codes and include an interaction term) The three different models imply different patterns on the coefficients Patterns of Regression Coefficients:  Patterns of Regression Coefficients Discrepancy model: Both regressions should yield a negative coef for the husband and a positive coef for the wife (maximizing the difference) Similarity model: For dyads where salary W>H, positive coef for husband and neg coef for wife because in this region higher husband salary identifies couples closer to equality For dyads where salary W<H, neg coef for husband and pos coef for wife because in this region higher wives’ salary identifies couples closer to equality Patterns of Regression Coef:  Patterns of Regression Coef Superiority model For couples where W>H on salary, a larger positive coef for wive’s salary The main point is that each model implies a qualitatively different pattern of regression weights across the two regressions. Conclusion:  Conclusion The take home message is that nonindependence due to interaction does not require a “statistical cure” Nonindependence provides an opportunity to measure and model social interaction Follow your conceptual models and your research questions There is still much room for careful design in correlational research with couples

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