How to obtain bootstrap confidence intervals for standardized estimates of a complex sampling SEM?

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Anita Prinzie

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Aug 6, 2016, 7:47:59 AM8/6/16

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Goal:

Obtain bootstrap confidence intervals for the standardized estimates of a complex sampling SEM

Details:

I am trying to obtain 95% bootstrap confidence intervals for the standardized estimates of a complex sampling SEM.

The survey design uses resampling method bootstrapping and the SEM is estimated on the bootstrapped covariance matrices. Lavaan survey corrects SEM for the fact that respondents are sampled within municipalities (multi-stage sampling).

The parameterEstimates method provides 95% bootstrap confidence intervals for the non-standardized estimates but not for the standardized methods.

When using bootstrapLavaan to obtain 95% bootstrap confidence intervals for the standardized estimates the error "Failed creating sampling statistics".

Please find my R code below.

R code:

#Complex survey design with resampling method bootstrap

des.gemeente <- svydesign(ids = ~ï..Gemeente, probs = ~1, data = dataBert)

bdes.gemeente <- as.svrepdesign(des.gemeente,type="bootstrap", replicates=5000)

#Structural model

finstructmodel <- '

# latent variable definitions

CREA_L =~ CREA1 + CREA2 + CREA3 + CREA5 + CREA6 + CREA7

KNO_L =~ KNO2 + KNO3 + KNO4

PLA_L =~ PLA1 + PLA2 + PLA3 + PLA4 + PLA6 + PLA7

EAS_L =~ EAS1 + EAS2 + EAS3 + EAS4

USE_L =~ USE1 + USE2 + USE3 + USE4

COM_L =~ COM3 + COM4 + COM5 + COM6

# variances and covariances

CREA2 ~ ~ CREA3

PLA2 ~ ~ PLA7

PLA3 ~ ~ PLA4

EAS1 ~ ~ EAS3

EAS2 ~ ~ EAS3

USE1 ~ ~ USE4

USE2 ~ ~ USE3

COM4 ~ ~ COM6

EAS_L ~ ~ USE_L

#regressions

EAS_L ~ a*CREA_L + c*KNO_L + e*PLA_L

USE_L ~ b*CREA_L + d*KNO_L + f*PLA_L

COM_L ~ g*EAS_L + h*USE_L + i*CREA_L

# indirect effect

ind_ag := a*g

ind_bh := b*h

ind_cg := c*g

ind_dh := d*h

ind_eg := e*g

ind_fh := f*h

#total effects from 1st stage on COM_L in third stage

tot_CREA_COM := i+ind_ag+ind_bh

tot_KNO_COM := ind_cg+ind_dh

tot_PLA_COM := ind_eg+ind_fh

#total effect on COM_L in third stage

total := i+ind_ag+ind_bh+ind_cg+ind_dh+ind_eg+ind_fh

#total indirect effect

total_ind := total-i'

finstructfit <- sem(finstructmodel,data=dataBert,estimator = "MLM")

#Structural model on bootstrapped covariance matrices correcting for respondents being clustered within municipalities

fit.finstruct.surveyb <- lavaan.survey(finstructfit, bdes.gemeente, estimator = "MLM")

parameterEstimates(fit.finstruct.surveyb,ci = TRUE,level = 0.95, boot.ci.type = "perc",standardized=TRUE)

#parameterEstimates provides 95% bootstrap cfis for the non-standardized estimates but not for the standardized estimates (neither for std.LV, std.ALL nor std.nox)

standardizedSolution(fit.finstruct.surveyb)

#provides the standardized estimates without 95% bootstrap confidence intervals

#trying to obtain 95% bootstrap confidence intervals for the standardized estimates using bootstrapLavaan

out <- bootstrapLavaan(fit.finstruct.surveyb, R = 5000, FUN = function(x) {

standardizedSolution(x)$est}, verbose = TRUE)

#returns Error: failed creating sample statistics

Terrence Jorgensen

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Aug 6, 2016, 3:46:27 PM8/6/16

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Goal: Obtain bootstrap confidence intervals for the standardized estimates of a complex sampling SEM

The bootstrapLavaan() function let's you grab anything you want, but I don't think it will be that simple with complex survey data. See this previous post for links about the issues:

https://groups.google.com/d/msg/lavaan/ENdcEjYfCPI/2HKgjENMBQAJ

Assuming you can find out the best way to do it, you might need to implement your own bootstrapping algorithm.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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