Moderated moderation model with latent variables

[Iris Diekemper]

Hello everybody,

I'm currently writing my masterthesis and I'm stuck trying to calculate the moderated moderation. I never used R before, so I might have gone wrong all the way. This is my structure model:

This is my script by now (I added a few explanations as my variables are in german terms):

library(lavaan)

library(semTools)

meine.daten <- read.csv("Befragungsergebnisse3.csv", header = TRUE, sep = ';')

daten.inter <- indProd(...) #I could only find examples with three variables, so I'm not sure if this is the right funktion to use with my numerous variables?

# Mein Modell

mein.modell <- '

 

# Messmodell

QA =~ QA_1 + QA_2 +QA_3 + QA_4 + QA_5.2 + QA_6.2 + QA_7 #quantitative Anforderungen (workload)

I =~ I_1 + I_2 + I_3 + I_4 + I_5 + I_6 + I_7 + I_8 #Irritation (irritation)

W =~ W_1 + W_2 + W_3 + W_4 + W_5 #Wohlbefinden (well-being)

GF_FK =~ GF_FK_1.2 + GF_FK_2.2 + GF_FK_3.2 + GF_FK_4.2 + GF_FK_5 + GF_FK_6 + GF_FK_7 + GF_FK_8 + GF_FK_9 + GF_FK_10 #Selbstführung der Führungskraft (health-oriented self-management of the leader)

GF_MA =~ GF_MA_1 + GF_MA_2 + GF_MA_3 + GF_MA_4 + GF_MA_5 + GF_MA_6 + GF_MA_7 + GF_MA_8 #Selbstführung des Mitarbeiters (health-oriented self-management of the employee)

GMF =~ GMF_1 + GMF_2 + GMF_3 + GMF_4 + GMF_5 + GMF_6 + GMF_7 + GMF_8 + GMF_9 + GMF_10 #Mitarbeiterführung (health-oriented leadership behaviour)

KU =~ KU_1 + KU_2 + KU_3 + KU_4.2 + KU_5.2 + KU_6.2 #Kontrollüberzeugung (control conviction)

BQ =~ BQ_1 + BQ_2 + BQ_3 + BQ_4 + BQ_5 + BQ_6 + BQ_7 + BQ_8 + BQ_9 + BQ_10 + BQ_11 + BQ_12 #Beziehungsqualität (relationship quality)

#Interaktionen

QA.GMF =~ QA:GMF

QA.GF_MA =~ QA:GF_MA

I.GMF =~ I:GMF

I.GF_MA  =~ I:GF_MA

QA.GMF.BQ =~ QA.GMF:BQ

QA.GF_MA.KU  =~ QA.GF_MA:KU

I.GMF.BQ =~ I.GMF:BQ

I.GF_MA.KU =~ I.GF_MA:KU

# Strukturmodell

GF_MA ~ GF_FK + GMF

GMF ~ GF_FK

I ~ QA + QA.GMF.BQ + QA.GF_MA.KU

W ~ I + I.GMF.BQ + I.GF_MA.KU'

# Modell analysieren

ergebnis <- sem(model=mein.modell, data=daten.inter, estimator='mlr')

summary(ergebnis, fit.measures=TRUE, standardized=TRUE)

Running my code as is (without the indProd function) I get the error:

Warning messages:

1: In lav_model_vcov(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  :

  lavaan WARNING:

    Could not compute standard errors! The information matrix could

    not be inverted. This may be a symptom that the model is not

    identified.

2: In lav_test_yuan_bentler(lavobject = NULL, lavsamplestats = lavsamplestats,  :

  lavaan WARNING: could not invert information matrix

Is this the right way to calculate my SEM? (My number of observations is 168)

I'm thankful for any suggestions!

[Christopher David Desjardins]

First, with 168 observations you probably shouldn't be fitting this model. That's not very many observations for the number of parameters you're estimating. You might be down to like 2:1 or 3:1 for number of subjects/parameter estimated.

Second, as far as I knew you can't create interactions between latent variables in lavaan doing this:

QA.GMF =~ QA:GMF

Instead, look at the indProd() function in the semTools package for creating products of indicators and I would consider double-mean centering. See this paper[1], which is cited b the indProd() function.

This thread, https://groups.google.com/forum/#!topic/lavaan/19ATRohxJTI, may also be helpful, in particular Ed's comments.

Chris

[1]: Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies. Structural Equation Modeling, 17(3), 374–391. doi:10.1080/10705511.2010.488999

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[Terrence Jorgensen]

look at the indProd() function in the semTools package for creating products of indicators and I would consider double-mean centering. 

Also see the functions probe3WayMC() and probe3WayRC() in semTools.  The nlsem package offers LMS estimation, but it is quite a tedious effort and estimation takes some time.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Iris Diekemper]

Thank you very much to both of you. I really appreciate it!