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Nested Example Using SPSS David A. Kenny January 8, 2014

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Presumed Background Multilevel Modeling

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Example Kashy (1991) Study of Gender and Intimacy respondents completed a survey each night for two weeks outcome is the average intimacy rating of each interaction partner(from 1 to 7, bigger numbers more intimacy) Levels level 1: intimacy of the interaction (1-7), partner gender (-1=male; 1=female) level 2: respondent gender (-1=male; 1=female) 3

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Download Data Syntax Output 4

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Equations A “separate” regression equation for each level 2 unit: Level 1 equation Intimacy = b 0 (intercept) + b 1 (partner gender) + error 1 The coefficients from the level 1 equation become the “dependent” variables: Level 2 equations b 0 = “average” intercept + effect of respondent gender + error 2 b 1 = “average” effect of partner gender + effect of respondent gender + error 3 Note that the effect respondent gender on the slope, b 1, for partner gender is the interaction of the two gender variables. 6

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Predicting Intimacy with Partner’s Gender for Each Participant Men ID Intercept (b 0i ) Slope (b 1i ) Number of Partners 1 5.35.76 11 2 3.39-.14 8 …. 26 4.41.37 14 Mean 3.85.24 Women 27 4.49-.11 35 28 4.03.03 22 … 77 4.40.32 19 Mean 4.39 -.16 7

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Effects Fixed Effects “average” intercept (b 0 ; like a grand mean) effect of respondent gender “average” slope (b 1 ; partner gender) interaction of partner and respondent gender Random effects variance error variance intercept or b 0 variance slope or b 1 variance covariance: intercept with slope 8

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Centering and the Example: Effects Coding Partner gender and respondent gender effects coded (-1 = male, +1 = female): overall intercept: respondents’ typical level of intimacy across both females and males intercept variance: differences in respondent’s typical level of intimacy across females and males overall slope: overall effect of partner gender across female and male respondents slope variance: differences in the effect of partner gender Note with effects coding, all effects are one-half the relative “advantage” or “disadvantage” of females over males because the difference between females and males is two units. 9

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Syntax MIXED intimacy WITH resp_gender partner_gender /FIXED = resp_gender partner_gender resp_gender*partner_gender /PRINT = SOLUTION TESTCOV /RANDOM INTERCEPT partner_gender | SUBJECT(id) COVTYPE(UNR). 17

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Random Effects 18

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Testing Variances in SPSS In SPSS all tests of variances are two- tailed. There is no interest in whether the variance is less than zero (in fact, the variance cannot never be less than zero). We can cut the p value in half for the variances. 19

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Example: Random Effects (in words) There is variation in the intercept: Some people say that they are more intimate than do others. Proportion of variance (intraclass correlation) due to the intercept:.852973/(.852973+ 1.890825) =.311. Variation due to partner gender not significant (p =.167) and could be dropped from the model. 20

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Example: Fixed Effects 21 df can be non-integer!

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Fixed Effects (in words) Females say that their interactions are more intimate than males by about half a point. (Remember with effects coding the difference between a man and a woman is two.) People say interactions with females are more intimate by about a tenth of a point, but this difference is not statistically significant. Mixed-gendered interactions (MF & FM) are viewed as more intimate than same-gendered interactions (MM & FF) by about a third of a point. 22

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Cell Means /EMMEANS=TABLES(overall) WITH (resp_gender=1 partner_gender=1) /EMMEANS=TABLES(overall) WITH (resp_gender=1 partner_gender=-1) /EMMEANS=TABLES(overall) WITH (resp_gender=-1 partner_gender=1) /EMMEANS=TABLES(overall) WITH (resp_gender=-1 partner_gender=-1) 23

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Fractional Degrees of Freedom Degrees of freedom are fractional because standard errors are variances that are pooled across levels. Method called Satterthwaite approximation. 26

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Centering and the Example: Dummy Coding Partner gender and respondent gender dummy coded (0: males; +1: females): overall intercept: male respondents’ typical level of intimacy with male partners intercept variance: differences in respondent’s typical level of intimacy with male partners overall slope: effect of partner gender for male respondents Note with dummy coding, all effects are the relative “advantage” or “disadvantage” of female over males. 27

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Thanks! Debby Kashy 28

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29 More Webinars References Programs Growth Curve Repeated Measures Two-Intercept Model Crossed Design Other Topics

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