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

DownloadDataSyntaxOutput

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Equations A “separate” regression equation for each level 2 unit:Level 1 equationIntimacy = b0(intercept) + b1(partner gender) + error1

The coefficients from the level 1 equation become the “dependent” variables:Level 2 equations•b0 = “average” intercept + effect of respondent gender + error2

•b1 = “average” effect of partner gender + effect of respondent gender + error3

Note that the effect respondent gender on the slope, b1, for partner gender is the interaction of the two gender variables. 

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Predicting Intimacy with Partner’s Gender for Each Participant

Men

ID Intercept (b0i) Slope (b1i) 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

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EffectsFixed Effects

“average” intercept (b0; like a grand mean) effect of respondent gender “average” slope (b1; partner gender) interaction of partner and respondent

genderRandom effects

variance error variance intercept or b0 variance slope or b1 variance

covariance: intercept with slope8

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).

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Random Effects

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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.

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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.

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Example: Fixed Effects

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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.

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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)

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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.

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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.

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Thanks! Debby Kashy

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More WebinarsReferences

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Two-Intercept Model

Crossed Design

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