1. Nested Example Using SPSS
David A. Kenny

2. 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)

4. Equations A “separate” regression equation for each level 2 unit:
Level 1 equation
Intimacy = 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.

5. Predicting Intimacy with Partner’s Gender for Each Participant
Men ID Intercept (b0i) Slope (b1i) Number of Partners … Mean Women … Mean

6. Effects Fixed Effects “average” intercept (b0; like a grand mean)
effect of respondent gender
“average” slope (b1; partner gender)
interaction of partner and respondent gender
Random effects
variance
error variance
intercept or b0 variance
slope or b1 variance
covariance: intercept with slope

7. 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.

15. 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).

16. Random Effects

17. 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.

18. 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.

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

20. 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.

21. 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)

24. 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.

25. Output from Other Programs
HLM X = part_gen
SAS Z = resp_gen
R: lmer
MLwiN

26. HLM: Formulation

27. HLM

28. SAS

29. R: lmer

30. MLwiN

31. Thanks!
Debby Kashy