On page 179-181, a new and much better power program is available as an app PowAPIMR.R and this program was written by Robert Ackerman. .
On page 156, the between and within results from the null model
are reversed. For the between regression, the SSerror is 33.24 and MSE =
1.75. For the within regression, the SSerror = 119 and the MSE = 5.95. (Thanks to Dorothy Bishop for telling us about this error.)
On the page 169, the chi square difference test of equal actor and partner effects should be 12.14, not 12.06.
The figure heading for Figure 7.3 on the page 171 should be "Campbell et al." and not "Simpson et al." Also in that figure the paths from Em and Ef should be be one.
On the bottom of page 176 and top of 177, there are two sets of SPSS syntax. For both, the " | NOINT " goes on the /FIXED line. For the set of SPSS syntax of page 177, the second line should be:
On pages 179-181, one should no longer use this method for computing power. A web based app written by Rob Ackerman and David Kennny called APIMPower can be used. A paper describing their approach to power should be available soon.
DISTRESS BY GENDER WITH ACT_NEURO PART_NEURO
Again the " | NOINT " goes on the /FIXED line.
On page 180, in the two equations, there should be some space between the plus sign and the lines on either side.
On page 183, we mean NLMIXED not NMIXED.
View a webinar introduction to the
Actor-Partner Interdependence Model and other webinars for its estimation. There is a small charge if you view more than one webinar.
Several APIM web-based apps are available that each provide text, tables, and figures that can be downloaded. They are APIM_MM for a regular APIM analysis esimated using multilevel modeling (download documentation here), APIM_SEM for a regular APIM analysis estimated structural equations modeling written by Lara Stat of Ghent University, APIMeM for a APIM mediation analysis (download documentation here), APIMoM for a APIM moderation analysis (download documentation here), and APIMPowerRdis for an APIM power analysis, written with Robert Ackerman.
Ledermann, Macho, and Kenny (2011) in the journal Structural Equation Modeling discuss mediation of the APIM. Also Kenny and Ledermann (2010) in the Journal of Family Psychology discuss a new index called k that quantifies the difference between various APIMs. Garcia, Kenny, and Ledermann(2015) in the journal Personal Relationships discuss moderation of the APIM. Ledermann and Kenny (2017) in the journal Personal Relationships discuss relative merits of using SEM versus multilevel modeling to estimate and test the APIM.
The APIM estimated by SEM with distinguishable dyads (p. 178-179) is a saturated model and so it has zero degrees of freedom and no measures of fit can be computed. Normally in SEM with latent variables, models have non-zero degrees of freedom and are over-identified. The use of SEM to estimate the APIM is to estimate two regression equations with correlated error terms. It is then not problematic that the base model is saturated and no measures of fit can be obtained.
It is possible to test for indistinguishability using MLM. Click here to download a document that describes how to do this. One might also want to consider a model of Partial Distinguishability: Actor and partner effects are equal for the two members but the intercepts and error variances may differ.
When using SEM, there are usually fit statistics such as the RMSEA or the CFI. However, the RMSEA can be misleading when the df are small. For example, Marga Korporaal found a chi square of 2.098 with 1 degree of freedom and an RMSEA =.126. As the example shows, a non-significant chi square can yield a large RMSEA (Kenny, Kaniskan, & McCoach, 2015, Sociological Methods and Research). Note also sometimes the CFI can be very small, despite good fit, if the relationships between variables are not strong. For these reasons, fit measures need not be reported for SEM-APIM analyses.
When conducting an APIM within multilevel modeling, one may wish to know the standardized or beta weight. One can use the Z-score option in SPSS on the pairwise data set. To this click: Analyze, Descriptive, then select the variables you want Z scored, and then click the box "save Z scores". One then runs the analysis using these new variables.
When using structural equation modeling with distinguishable dyads as in Figure 7.3, it is advisable to estimate the intercepts for each of the members on the outcome variable. For the example, the difference in intercepts estimates the gender difference. It is then important that causal variables have a meaningful zero and if not they should be centered.
How do you compute R squared when dyad members are distinguishable, say by gender, when using multilevel modeling? For distinguishable dyads, there are two error variances, one for males and one for females, assuming you have asked for heterogeneous variance by using CSH with SAS or SPSS. There are two R squared values, one for the males and one for the females. For each, you would compute 1 - [EV(M)/EV(E)] where EV(M) is the error variance for the model with the actor and partner effects and EV(E) is the empty model, a model with no actor and partner effects. However, for the empty model, it is advisable to have gender in the model, so it is not entirely "empty."
One should not use the standardized estimates when using SEM. Rather, to obtain standardized estimates, the following strategy can be employed. Using the pairwise or individual dataset compute the means and standard deviations. Alternatively, average the male and female means and variances. (This second strategy results in slightly different variances.) Now using the overall means and standard deviationss, standardize the data. Then redo the SEM runs. From this run, report the unstandardized coefficients as the standardized coefficients are still "wrong" (this seems odd, but this is what you do).
A decomposition of nonindependence is discussed in a handout written by David Kenny.
Campbell et al.
Data and Files
Artificial Roommate Data in Table 7.1
SPSS (Page 161):
SAS (Page 160):
MLwin (Page 165):
Run of the Roommate Data
HLM (Page 164):
HLM File, and
Campbell et al. Study: Page 171-177 (There appears to be minor error in the centering of neuroticism which changes the intercepts in some analyses.):
Campbell et al. Dyad Data