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HLTH 653 Lecture 3: Moderator Variables Raul Cruz-Cano Spring 2013 HW#1 • Different datasets • P-values • Correlation: High level vs. Significant Moderator • • A moderator is a variable that influences the strength or the direction of a relationship between a predictor variable and a criterion variable. In general terms, a moderator is a qualitative (e.g., sex, race, class) or quantitative (e.g., level of reward) variable that affects the direction and/or strength of the relation between an independent or predictor variable and a dependent or criterion variable. Moderator Predictor a b Predictor Outcome moderators and predictors are at the same level in regard to their role as causal variables Moderator c Predictor * Interactor Outcome Moderator: Example • • • Suppose a researcher finds that familial stress (e.g., in the context of a child’s chronic illness) is negatively associated with child psychological adjustment. Although this finding may be of interest to the researcher, it may be that the effect becomes more or less robust in the presence of other contextual variables. In fact, the researcher may develop specific theories about conditions that determine the strength of the relationship between stress and adjustment. – For example, the strength or the direction of the relationship between stress and adjustment may depend on the type of coping used by the family. – That is, a significant association may emerge only when a child copes in a maladaptive manner. – By testing coping style as a moderator of the relationship between stress and outcome, the researcher can specify certain conditions under which family stress predicts child adjustment. – This would not only allow for more precise conclusions, but would likely have implications for future interventions. Moderator: Example – For example, the strength or the direction of the relationship between stress and adjustment may depend on the type of coping used by the family. Coping Style Family Stress Child Adjustment Example: Quittner, 1992 • • • • Study the role of social support in the relationship between parenting-related stress and psychological distress in parents of children with hearing impairment and seizure disorder. Parenting stress is more likely to have adverse effects on adjustment when parents have low levels of social support (i.e., social support is a moderator)? Quittner found that the relationship between parental stress and psychological distress did not vary as a function of level of social support. Put another way, social support did not moderate or alter the strength or direction of the relationship between parental stress and psychological distress. Social Support Parenting Stress Psychological Distress in Parents Example: Stem, McCants and Pettine (1982) • Found that the positivity of the relation between changing life events and severity of illness was considerably stronger for uncontrollable events (e.g., death of a spouse) than for controllable events (e.g., divorce). “Controlability“ of Event life-event change likelihood of illness Test for Moderator Hypotesis Glass and Singer's (1972) Predictor: Noise Level Moderator: Periodic-Aperiodic noise Predictor x Interactor a b Task Performance c Test for Moderator Hypothesis • The model diagrammed has three causal paths: – The impact of the noise intensity as a predictor (Path a), – The impact of controllability as a moderator (Path b), and – The interaction or product of these two (Path c). • The moderator hypothesis is supported if: 1. 2. 3. the interaction (Path c) is significant to predict the outcome or significantly correlated with it the moderator variable is uncorrelated with the predictor the moderator variable is uncorrelated with the criterion (the dependent variable) • There may also be significant main effects for the predictor and the moderator (Paths a and b), but these are not directly relevant conceptually to testing the moderator hypothesis. What does it mean if condition 2 is not met? What does it mean if condition 3 is not met? SAS Example 1: Rural Women HIV Study • The cross-sectional data were collected in the first of three interviews of a longitudinal study designed to test the efficacy of a peer counseling intervention designed for rural women with HIV disease. • Tested a peer-based social support intervention designed for a population of rural women with HIV disease • The 280 study participants were recruited from 10 community-based HIV/AIDS service organization serving rural areas of the southeastern United States. • Study participants were randomly assigned to intervention and control groups. • Intervention group participants received a total of 12 face-to-face peercounseling sessions over a period of six months, while the control group received the usual care provided by the agency by which they were recruited. • Peer counselors were recruited at each local study site to implement the intervention. SAS Example1: Rural Women HIV Study • Tavakoli, A., Jackson, K., & Moneyham, L. (2009) • The moderator effect was examined. • The regression model included – – – – Reason Missing of Medication (Outcome Variable) Available social support (Predictor=Path a) Spiritual activities (Mediator=Path b) Their interaction effect (Interaction=Path c) • A moderator effect exist if the interaction term explains a statistically significant amount of variance of criterion variable. SAS Example1: Rural Women HIV Study • Variables: – – – – Available Social Support (TSSQAV) Spiritual Activities (TCOPESA) Reason Missing of Medication (TREAS) Interaction (SSCOPESA) Title ' Regression model / testing moderator effect' ; proc reg data=two; model treas = tssqav tcopesa sscopesa/ stb pcorr2 scorr2; run; STB: displays standardized parameter estimates PCORR2: displays squared partial correlation coefficients computed using Type II sums of squares SCORR2 : displays squared semipartial correlation coefficients computed using Type II sums of squares SAS Example1: Rural Women HIV Study SAS Example1: Rural Women HIV Study • The result did not reveal any moderator effect for available social support and spiritual activities (P-value=0.51), i.e. condition 1 was not met SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children • Tavakoli, Scharer & Hussey, L. (2011) • This study examines the role of perceived stress in the relationship between social support and mood, and tested if moderator effects influenced the relationship. • The role of coping in the relationship between perceived stress and mood was also examined for potential moderator effects. • The cross-sectional data reported here were collected in an experimental design with repeated measures with mothers of children who had been hospitalized on a child psychiatric unit. • A convenience sample of mothers was randomly assigned into three groups: A web-based intervention group, a telephone social support intervention group, and a usual care group. • The moderator effect was examined by including interaction effect in the regression model. SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children • Variables: Perceived stress (TPSS) as moderator of social support (TSS) to mood (POMSMOD) • TPSSSS= Interaction proc reg data=two; model pomsmod = tpss tss tpssss / stb pcorr2 scorr2; run; SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children • The result did not reveal any moderator effect for social support and perceived stress (Pvalue=0.4878), i.e. condition 1 was not met SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children • Variables: Coping (TCOPE) as moderator perceived stress (TPSS) to mood (POMSMOD) • TPSSCOP = Interaction proc reg data=two; model pomsmod = tcope tpss tpsscop / stb pcorr2 scorr2; run; SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children SAS Example 2: Moderator Effect for Social Support of Mothers of Mentally Ill Children • The result did not indicate any moderator effect for perceived stress and coping (Pvalue=0.1004), condition 1 was not met SAS Example 3: Attitudes About Animals • Ethical idealism as a dichotomous moderator variable • Dichotomy was produced by classifying cases with idealism scores greater than the median as being “idealistic” and those with scores less than or equal to the median as being “nonidealistic.” • The attitude towards animal rights and animal research scale used consisted of 28 items • Item-total correlations were good, in other words, these 28 items were internally consistent, all measuring the same basic construct. One containing items reflecting concern with the violation of animal rights by using animals for food, clothing, and fur (AR=Support of Animal Rights). • Misanthropy is the general hatred, mistrust or disdain of the human species or human nature. SAS Example 3: Attitudes About Animals • Hypothesized that misanthropy would be less strongly related to support for animal rights among idealists Idealism Misanthropy Support of Animal Rights Run Moderate.sas SAS Example 3: Attitudes About Animals • Moderator variable, idealism, is not significantly related to either misanthropy or support of animal rights. – Correlation between Idealism and AR = 0.03 – Correlation between Idealism and Misanthropy = -0.14 – Conditions 2 and 3= • While ethical idealism may not be related to support of animal rights here, it may moderate the relationship between misanthropy and support of animal rights. – Condition 1= ? SAS Example 3: Attitudes About Animals ZAR =.303ZMisanth + .067ZIdeal .146 Zinteraction -.02 Model: • R-Square =0.1130 • p-value=0.0004 p = .049 All this evidence indicates that ethical idealism does function as a moderator of the relationship between misanthropy and support of animal rights Who moderates who? • Remember a lot is based on correlations, hence causality is kind of tricky…. Other options • Subgroup analysis: In subgroup analysis, to identify the moderator variable, the sample is split into subgroups on the basis of the third variable. In this method, to identify the moderator variable, regression analysis is employed to investigate the relationship between the predicator variable and the criterion of each subgroup variable. R2 measures the presence or absence of the moderator variable. • Moderated regression analysis (MRA): This is a regression based technique that is used to identify the moderator variable. (1) (2) (3) Z=Moderator Other Cases 1. Moderator continuous, independent continuous, dependent continuous =>We just studied 2. Moderator dichotomous, independent dichotomous, dependent continuous => 2x2 ANOVA (with interaction term) for condition 1, one-way ANOVA for conditions 2 and 3 PROC ANOVA DATA = dental; class A B; model relief = A B A*B; RUN; Other Cases 3. Moderator is a dichotomy, independent variable is a continuous, dependent continuous => conditions 2 and 3 the same as in class, for condition 1: correlate independent variable with outcome variable separately for each value of the moderator and then test the difference Other Cases 4. Moderator is a continuous variable, the independent variable is a dichotomy =>Depends on the effect Reuben M. Baron and David A. Kenny, The Moderator-Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations, Journal of Personality and Social Psychology, 1986, Vol. 51, No. 6, 1173-1182 Dichotomous DV • What if the DV is dichotomous (e.g., group membership, voting decision etc.)? • Use moderated logistic regression (Jaccard, 2001) Logit ( ) b 0 b 1 X b 2 M b 3 X M In summary… Continuous DV Dichotomous DV moderated logistic regression Independent Continuous Dichotomous Moderator Continuous Dichotomous Class #1 #3 #4 #2 References • • • • • • • Quittner, AL. Re-examining research on stress and social support: the importance of contextual factors. In: La Greca AM, Siegel LJ, Wallander JL, Walker CE, eds. Stress and Coping in Child Health. New York: Guilford Press; 1992:85– 115. Stern, G. S., McCants, T. R., & Pettine, P. W. (1982). The relative contribution of controllable and uncontrollable life events to stress and illness. Personality and Social Psychology Bulletin, 8, 140145. Glass, D., & Singer, J. (1972). Urban stress: Experiments on noise and social stressors. New York: Academic Press. Tavakoli, A., Jackson, K., & Moneyham, L. (2009). Examining Mediator and Moderator effect using Rural Women HIV Study. SAS Global Forum. March 21-25, Washington DC. Abbas S. Tavakoli, DrPH, MPH, ME; Kathleen Scharer, PhD, RN, PMHCNS-BC, FAAN; & Jim Hussey, PhD, Compare Imputation and no Imputation to Examine Mediator Effect for Social Support of Mothers of Mentally Ill Children , SAS Global Forum 2011 Wuensch, K. L., Jenkins, K. W., & Poteat, G. M. (2002). Misanthropy, idealism, and attitudes towards animals. Anthrozoös, 15, 139-149. James Jaccard , Interaction Effects in Logistic Regression, Issue 135, Quantitative Applications in the Social Sciences, Volume 135 of A Sage university paper, Sage university papers series. no. 07-135, Issue 7, Part 135 of Sage university papers series: Quantitative applications in the social sciences Interaction Effects in Logistic Regression, Interaction Effects in Logistic Regression