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

Presumed Background Multilevel Modeling

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

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

Predicting Intimacy with Partner’s Gender for Each Participant Men ID Intercept (b 0i ) Slope (b 1i ) Number of Partners … Mean Women … Mean

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

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

Random Effects 18

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

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: /( ) =.311. Variation due to partner gender not significant (p =.167) and could be dropped from the model. 20

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

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

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

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

Thanks! Debby Kashy 28

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