sim () function produces warning about negative ov variances

[Elisabeth Zureck]

Dear all,
I'm trying to run a power analysis for a latent mediation model using the simsem package.

I defined my population (based on lavaan output on piolot data indicating good overall fit) and my analysis models as follows:

population.model <- "WB  =~ 1*gs.ind1  + 1.004*gs.ind2
                      EXT =~ 1*ext.ind1 + 0.757*ext.ind2
                      AUF =~ 1*auf.ind1 + 1.103*auf.ind2

                      WB ~ 0.051*EXT + 0.580*AUF
                      AUF ~ 0.302*EXT

                      gs.ind1  ~ 3.911*1
                      gs.ind2  ~ 3.860*1
                      ext.ind1 ~ 3.918*1
                      ext.ind2 ~ 3.660*1
                      auf.ind1 ~ 3.236*1
                      auf.ind2 ~ 3.099*1
                      WB  ~ 0*1
                      EXT ~ 0*1
                      AUF ~ 0*1
                     
                      gs.ind1  ~~ 0.061*gs.ind1
                      gs.ind2  ~~ 0.123*gs.ind2
                      ext.ind1 ~~ 0.096*ext.ind1
                      ext.ind2 ~~ 0.420*ext.ind2
                      auf.ind1 ~~ 0.155*auf.ind1
                      auf.ind2 ~~ 0.050*auf.ind2
                      WB  ~~ 0.323*WB
                      EXT ~~ 0.603*EXT
                      AUF ~~ 0.285*AUF"



analysis.model  <- "WB =~ gs.ind1 + gs.ind2
                    EXT =~ ext.ind1 + ext.ind2
                    AUF =~ auf.ind1 + auf.ind2

                    WB ~ c*EXT + b*AUF
                    AUF ~ a*EXT
                    indirekt := a*b
                    total := a*b + c"

Afterwards I tried to simulate data and model the analysis data with varying sample sizes to estimate the power:
med.n <- sim(model=analysis.model, n = rep(seq(50,200,10),10), generate = population.model,
             lavaanfun = "sem", std.lv=FALSE)

This analysis resulted in 50 warnings:

50: In lav_object_post_check(object) :
  lavaan WARNING: some estimated ov variances are negative

Do you have any ideas what might be wrong about my models?
Thank you in advance for your help!

[Terrence Jorgensen]

Do you have any ideas what might be wrong about my models?

Probably nothing.  You have specified some residual variances that are very close to zero (e.g., auf.ind2 ~~ 0.050*auf.ind2), and you have some very small sample sizes (as low as N = 50).  So estimates of near-zero variances are quite likely to be negative in several samples just due to sampling error.  Try looking at the M and SD of the sampling distribution of that estimate across replications -- you can probably guess that sometimes it is going negative.

Because you know the cause is just sampling error, you don't need to worry about it.  If it were a single real data set, you would want to test whether the negative variance is consistent with sampling error (if not, then model misspecification is the other alternative explanation).

http://journals.sagepub.com/doi/abs/10.1177/0049124112442138

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

[Elisabeth Zureck]

Dear Terrence,
Thank you very much for your explanation. I will look at the sampling distribution of my ov residual variances.
Best Elisabeth