Nested Example Using SPSS David A Kenny January

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

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)

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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.

Predicting Intimacy with Partner’s Gender for Each Participant Men ID 1 2 Intercept (b 0 i) Slope (b 1 i) Number of Partners 5. 35 . 76 11 3. 39 -. 14 8 …. 4. 41 . 37 14 3. 85 . 24 26 Mean Women 27 4. 49 -. 11 28 4. 03 … 77 4. 40 . 32 Mean 4. 39 -. 16 35 22 19 5

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

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.

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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). 15

Random Effects

Testing Variances in SPSS • In SPSS all tests of variances are twotailed. • 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. 17

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.

Example: Fixed Effects df can be non-integer! 19

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.

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) 21

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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.

Output from Other Programs HLM X = part_gen SAS Z = resp_gen R: lmer MLwi. N

HLM: Formulation 26

HLM 27

SAS 28

R: lmer 29

MLwi. N 30

Thanks! Debby Kashy