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Dec 17, 2016, 2:23:37 PM12/17/16

to lavaan

Hi

I am carry out a mediation structural model and have received the below warning. What does this mean and how can I correct this? Full syntax is attached.

Thanks very much!

> SCTModel2
<- '

+ RBehF1=~BF1_RAV+BF2_RAV+BF3_RAV+BF4_RAV+BF6_RAV+BF7_RAV

+ RJobSat=~RaterJobSat

+ RReward=~RaterReward

+ #
direct effect

+ RaterJobSat
~ c*RBehF1

+ #
mediator

+ RaterReward
~ a*RBehF1

+ RaterJobSat
~ b*RaterReward

+ #
indirect effect (a*b)

+ indirect
:= a*b

+ #
total effect

+ total
:= c + (a*b)

+ RBehF1~~RaterJobSat

+ RBehF1~~RaterReward

+ RaterReward~~RaterJobSat

+ '

>

> SCT1fit2<-sem(SCTModel2,
data = SMBI_Alldata, test = "bollen.stine", se="boot", bootstrap = 5000)

Warning
message:

In
lav_object_post_check(lavobject) :

lavaan WARNING: the covariance matrix of the
residuals of the observed

variables (theta) is not
positive definite;

use
inspect(fit,"theta") to investigate.

__ __

__ __

`inspect(SCT1fit2,"theta") `

` BF1_RA BF2_RA BF3_RA BF4_RA BF6_RA BF7_RA RtrJbS RtrRwr`

`BF1_RAV 0.038 `

`BF2_RAV 0.000 0.029 `

`BF3_RAV 0.000 0.000 0.030 `

`BF4_RAV 0.000 0.000 0.000 0.041 `

`BF6_RAV 0.000 0.000 0.000 0.000 0.026 `

`BF7_RAV 0.000 0.000 0.000 0.000 0.000 0.040 `

`RaterJobSat 0.000 0.000 0.000 0.000 0.000 0.000 0.000 `

`RaterReward 0.000 0.000 0.000 0.000 0.000 0.000 0.117 0.000 `

__ __

__ __

Dec 17, 2016, 6:59:34 PM12/17/16

to lavaan

What does this mean and how can I correct this?

You can find out what an NPD matrix is with a quick Google search. Here is a quite informative page:

It doesn't necessarily need "correction", if sampling variability is a better explanation than model misspecification. Concluding so requires (a) your model fits well and (b) the 95% CI for the Heywood case includes plausible values. Here is an article on the topic:

But in your specific case, I would guess the problem is that you are modeling the relationship between RaterJobSat and RaterReward twice (as a regression path "b" and as a residual covariance), which is a particularly odd choice because you are using them as single indicators of latent constructs:

RJobSat=~RaterJobSat

RReward=~RaterReward

RaterJobSat ~ b*RaterReward

RaterReward~~RaterJobSat

I'm surprised lavaan even converged on a solution, because this model is not identified. Regardless, your theta matrix is NPD because it is impossible for two variables (here, "residuals" of RaterJobSat and RaterReward) to *co*vary (i.e., to vary together) when they don't even vary.

RtrJbS RtrRwr

RaterJobSat 0.000`RaterReward 0.117 0.000`

If there is a regression between those variables, then there is no need to additionally estimate a correlation between their residuals (likewise for both of those with RBehF1). And if you are using them as single indicators, then you should estimate the regression path between the latent variables, not between the indicators.

SCTModel2 <- 'RBehF1 =~ BF1_RAV + BF2_RAV + BF3_RAV + BF4_RAV + BF6_RAV + BF7_RAVRJobSat =~ RaterJobSatRReward =~ RaterReward# direct effectRJobSat ~ c*RBehF1# mediatorRReward ~ a*RBehF1RJobSat ~ b*RReward# indirect effect (a*b)indirect := a*b# total effect

total := c + (a*b)

'

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

Feb 25, 2019, 5:24:57 AM2/25/19

to lavaan

Hi Terrence Jorgensen,

How do we determine "(b) the 95% CI for the Heywood case includes plausible values."? Is it located in the summary of our model ?

Best,

Camille Williams

Feb 28, 2019, 10:10:37 PM2/28/19

to lavaan

How do we determine "(b) the 95% CI for the Heywood case includes plausible values."? Is it located in the summary of our model ?

yes, that is an option

`summary(fit, ci=TRUE)`

Or you can use the parameterEstimates() function.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

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