Mediator effect - problem with direct, indirect and total effect

[Ana Carolina Sauer Liberato]

Hello everyone, 

I believe I can use a little of your expertise with lavaan. 

I am running this model in which I am evaluating the mediating effects (SE, OE, SMB and KSA) between intervention and outcomes (latent variables of physical and psychological).

I was pretty happy with my model in code 1. However I decided to change a little to make easier to see direct, indirect and total effect (Code 2) according to a code that i found in a book. The problem is that I am having now 2 different results with code 1 and code 2 (different fit and loading) and I believe they were suppose to be the same. 

 

Code 1:

Intervention_all_mediators<- '

Psychological =~ 

SF.MentalHealth_T.3_rescale + 

SF.RoleEmotional_T.3_rescale + 

SF.SocFunct_T.3_rescale + 

STAI_3months_TS_Rescale  +

PHQ_3months_TS

physical =~   

SF.PhysFunct_T.3_rescale + 

SF.RolePhys_T.3_rescale + 

SF.BodilyPain_T.3_rescale + 

PCA_3months_Rescale

#SE portion

SE =~  SE_3Months

SE_3Months~~0*SE_3Months

SE ~ Psychological

SE ~ physical

#OE portion

OE =~ OE_3Months

OE_3Months~~0*OE_3Months

OE ~ Psychological

OE ~ physical

#SMB portion

SMB =~ SMB_dic_3Months_rescale

SMB_dic_3Months_rescale~~0*SMB_dic_3Months_rescale

SMB ~ Psychological

SMB ~ physical

#KSA portion

KSA =~ KSA_3Months_rescale

KSA_3Months_rescale~~0*KSA_3Months_rescale

KSA ~ Psychological

KSA ~ physical

# Intervention

Intervention =~ intervention_num

intervention_num ~~ 0*intervention_num

SE ~ Intervention

OE ~ Intervention

KSA ~ Intervention

SMB ~ Intervention

Psychological ~ Intervention

physical ~ Intervention

#Correlated error

SF.RolePhys_T.3_rescale ~~ PCA_3months_Rescale 

SF.MentalHealth_T.3_rescale ~~ PHQ_3months_TS

SF.MentalHealth_T.3_rescale ~~ STAI_3months_TS_Rescale 

SF.MentalHealth_T.3_rescale ~~  SF.SocFunct_T.3_rescale

SF.RoleEmotional_T.3_rescale ~~ SF.SocFunct_T.3_rescale

OE ~~ SE

KSA ~~ SE

Psychological ~~ physical

'

Intervention_out <- sem(Intervention_all_mediators, data = dataaim1

                        ,ordered=c("Intervention"))

summary(Intervention_out, standardized=TRUE, fit.measures=TRUE, rsq=TRUE, modindices = TRUE)

resid(Intervention_out, type = "cor")

semPaths(Intervention_out, whatLabels = "est")

varTable(Intervention_out)

Code 2: 

######direct, mediator, Indirect and total effect

model_DIT3M<- '

  

Psychological =~ 

SF.MentalHealth_T.3_rescale + 

SF.RoleEmotional_T.3_rescale + 

SF.SocFunct_T.3_rescale + 

STAI_3months_TS_Rescale  +

PHQ_3months_TS

physical =~   

SF.PhysFunct_T.3_rescale + 

SF.RolePhys_T.3_rescale + 

SF.BodilyPain_T.3_rescale + 

PCA_3months_Rescale

#SE portion

SE =~ SE_3Months

SE_3Months~~0*SE_3Months

#OE portion

OE =~ OE_3Months

OE_3Months~~0*OE_3Months

#SMB portion

SMB =~ SMB_dic_3Months_rescale

SMB_dic_3Months_rescale~~0*SMB_dic_3Months_rescale

#KSA portion

KSA =~ KSA_3Months_rescale

KSA_3Months_rescale~~0*KSA_3Months_rescale

# Intervention

Intervention =~ intervention_num

intervention_num ~~ 0*intervention_num

#Correlated error

SF.RolePhys_T.3_rescale ~~ PCA_3months_Rescale 

SF.MentalHealth_T.3_rescale ~~ PHQ_3months_TS

SF.MentalHealth_T.3_rescale ~~ STAI_3months_TS_Rescale 

SF.MentalHealth_T.3_rescale ~~  SF.SocFunct_T.3_rescale

SF.RoleEmotional_T.3_rescale ~~ SF.SocFunct_T.3_rescale

OE ~~ SE

KSA ~~ SE

Psychological ~~ physical

######direct, mediator, Indirect and total effect

#Direct effect

Psychological ~ e*Intervention

physical ~ d*Intervention

#Mediator

SE ~ a*Intervention

OE ~ f*Intervention

SMB ~ i*Intervention

KSA ~ l*Intervention

physical ~ b*SE

Psychological ~ c*SE

physical ~ g*OE

Psychological ~ h*OE

physical ~ j*SMB

Psychological ~ k*SMB

physical ~ m*KSA

Psychological ~ n*KSA

#Indirect effect

indirect_SE_Physical:= a*b

indirect_SE_Psychological:= a*c

indirect_OE_Physical:= f*g

indirect_OE_Psychological:= f*h

indirect_SMB_Physical:= i*j

indirect_SMB_Psychological:= i*k

indirect_KSA_Physical:= l*m

indirect_KSA_Psychological:= l*n

#Total effect

Total_SE_Physical:= d+(a*b)

Total_SE_Psychological:= e+(a*c)

Total_OE_Physical:= d+(f*g)

Total_OE_Psychological:= e+(f*h)

Total_SMB_Physical:= d+(i*j)

Total_SMB_Psychological:= e+(i*k)

Total_KSA_Physical:= d+(l*m)

Total_KSA_Psychological:= e+(l*n)

#Direct print

Direct_Psychological:= e

Direct_Physical:=  d

#Mediator print

Mediator_Psychological:= c

Mediator_Physical:= b

Mediator_SE := a

Mediator_OE := f

Mediator_SMB := i

Mediator_KSA := l

'

fit_DIT3M <- sem(model_DIT3M, data = dataaim1)

summary(fit_DIT3M, standardized=TRUE, fit.measures=TRUE, rsq=TRUE, modindices = TRUE)

semPaths(fit_DIT3M, whatLabels = "est")

[Terrence Jorgensen]

I am having now 2 different results with code 1 and code 2 (different fit and loading) and I believe they were suppose to be the same. 

fit_DIT3M <- sem(model_DIT3M, data = dataaim1)

You left out ordered=c("Intervention") from this sem() call, so this one used ML estimation, whereas the first used DWLS estimation (and the meaning of the Invervention variable is different).

If Intervention is binary, you can just represent it with a dummy code.  It is exogenous, so you don't need to make any distributional assumptions about it if you set fixed.x = TRUE (which is the default setting).

http://lavaan.ugent.be/tutorial/cat.html

You can also simplify your code by regressing the factors directly on your mediators.  You don't need to "put them into latent space" by creating 4 single-indicator constructs.  

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

[Ana Carolina Sauer Liberato]

Thank you so much Terry for your reply!