Multiple Causes and Indicators coding error (formative latent variables)

Daca 33

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Nov 21, 2014, 11:59:47 AM11/21/14

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Hi all,

I am trying to write the syntax for my model using the lavaan package in R and I am getting a rather long error message regarding my code.

I am not sure if I did this correctly given the path diagram (path diagram picture included in the attachment). I think my biggest problem is not knowing if I programmed my formative latent variables correctly.

In addition, I need to standardize coefficients for real GDP Growth (y2) and GDP per capita (y4). Does my code below currently do this for me or am I missing an important step?

Thank you in advance for help.

> data1 <- read.csv("/Users/demkic/Documents/R/specification1.csv", header=T)

>

> library(lava an)

This is lavaan 0.5-17

lavaan is BETA software! Please report any bugs.

> SE.Model <- '

+ #regressions

+ SE <~ X5 + X6 + X2 + X1

+ C <~ X7 + X11 + X10 + X8

+

+ #latent variable definitions

+ SE =~ Y2 + Y3 + Y1

+ C =~ Y4 + Y5 + Y6'

>

> fitSE <- sem(SE.Model, data = data1)

Warning messages:

1: In lav_data_full(data = data, group = group, group.label = group.label, :

lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others; use varTable(fit) to investigate

2: In lav_data_full(data = data, group = group, group.label = group.label, :

lavaan WARNING: small number of observations (nobs < nvar)

nobs = 8 nvar = 14

3: In lav_samplestats_from_data(lavdata = lavdata, missing = lavoptions$missing, :

lavaan WARNING: sample covariance can not be inverted

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

lavaan WARNING: could not compute standard errors!

lavaan NOTE: this may be a symptom that the model is not identified.

5: In lavaan::lavaan(model = SE.Model, data = data1, model.type = "sem", :

lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.

Screen Shot 2014-11-21 at 5.50.39 PM.png

Daca 33

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Nov 21, 2014, 12:09:01 PM11/21/14

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In addition here is my output:

> summary(fitSE, standardized=TRUE, fit.measures=TRUE)

lavaan (0.5-17) converged normally after 877 iterations

Number of observations 8

Estimator ML

Minimum Function Test Statistic 165.025

Degrees of freedom 50

P-value (Chi-square) 0.000

Model test baseline model:

Minimum Function Test Statistic 251.084

Degrees of freedom 63

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.388

Tucker-Lewis Index (TLI) 0.229

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) 96.711

Loglikelihood unrestricted model (H1) 179.224

Number of free parameters 19

Akaike (AIC) -155.423

Bayesian (BIC) -153.913

Sample-size adjusted Bayesian (BIC) -210.056

Root Mean Square Error of Approximation:

RMSEA 0.536

90 Percent Confidence Interval 0.447 0.628

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.171

Parameter estimates:

Information Expected

Standard Errors Standard

Estimate Std.err Z-value P(>|z|) Std.lv Std.all

Latent variables:

SE =~

Y2 1.000 0.038 0.858

Y3 0.085 0.003 0.472

Y1 1.125 0.042 0.951

C =~

Y4 1.000 1051.539 0.627

Y5 -0.001 -0.633 -0.981

Y6 -0.000 -0.219 -0.910

Composites:

SE <~

X5 -0.064 -1.694 -0.113

X6 -0.767 -20.362 -0.474

X2 0.173 4.606 1.137

X1 0.279 7.407 2.121

C <~

X7 215.516 0.205 0.015

X11 31.308 0.030 0.141

X10 -1046.114 -0.995 -0.353

X8 9748.954 9.271 0.742

Covariances:

SE ~~

C 1.879 Inf Inf

Variances:

Y2 0.001 0.001 0.264

Y3 0.000 0.000 0.777

Y1 0.000 0.000 0.096

Y4 1710726.574 1710726.574 0.607

Y5 0.016 0.016 0.038

Y6 0.010 0.010 0.173

SE 0.000 0.000 0.000

C 0.000 0.000 0.000

Edward Rigdon

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Nov 21, 2014, 12:40:38 PM11/21/14

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Your 14 observed variables produce 105 max Degrees of freedom for the covariance structure model. Your estimated model has only 50 degrees of freedom, so you are estimating105 - 50 = 55 parameters, based on 8 observations on 14 variables. The warning messages are just telling you that this is not going well, which is what one ought to expect. All of these warning messages can be tied to low sample size. That appears to be the central problem.

--Ed Rigdon

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Daca 33

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Nov 21, 2014, 5:04:40 PM11/21/14

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Thank you for the reply. I will add some more observations to my data

Based on my path diagram, is my model correctly specified below?

(I am having trouble finding literature in lavaan on how to code formative latent variables)

> SE.Model <- '

+ #regressions

+ SE <~ X5 + X6 + X2 + X1

+ C <~ X7 + X11 + X10 + X8

+

+ #latent variable definitions

+ SE =~ Y2 + Y3 + Y1

+ C =~ Y4 + Y5 + Y6'

thank you

Best,

Daria

yrosseel

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Nov 27, 2014, 1:44:48 PM11/27/14

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On 11/21/2014 11:04 PM, Daca 33 wrote:
> Thank you for the reply. I will add some more observations to my data
>
> Based on my path diagram, is my model correctly specified below?
> (I am having trouble finding literature in lavaan on how to code
> formative latent variables)
>
> > SE.Model <- '
> + #regressions
> + SE <~ X5 + X6 + X2 + X1
> + C <~ X7 + X11 + X10 + X8
> +
> + #latent variable definitions
> + SE =~ Y2 + Y3 + Y1
> + C =~ Y4 + Y5 + Y6'

No. You can 'define' the latent variables only once. I would create them
as reflective factors, and then add the regressions:

SE =~ Y2 + Y3 + Y1

C =~ Y4 + Y5 + Y6

E ~ X5 + X6 + X2 + X1

C ~ X7 + X11 + X10 + X8

Yves.

Daca 33

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Nov 30, 2014, 11:36:18 AM11/30/14

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Code:

SE.Model <- '

#regressions

SE ~ Businessreg + UnemplRate + Trans.Subs + Govconsump

C ~ GovEffect + FiscalFree + BeauCosts + RuleofLaw

#reflective factors

SE =~ RealGDP + LaborForce + M0M1

C =~ GDPperCapita + BribeIndex + Judicialind.'

fit <- sem(SE.Model, data = mydata)

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

After adding more data and following the advice below, the output I received is:

lavaan (0.5-17) converged normally after 604 iterations

Used Total

Number of observations 11 23

Estimator ML

Minimum Function Test Statistic 308.220

Degrees of freedom 48

P-value (Chi-square) 0.000

Model test baseline model:

Minimum Function Test Statistic 380.478

Degrees of freedom 63

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 0.180

Tucker-Lewis Index (TLI) -0.076

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -121.333

Loglikelihood unrestricted model (H1) 32.777

Number of free parameters 21

Akaike (AIC) 284.666

Bayesian (BIC) 293.022

Sample-size adjusted Bayesian (BIC) 229.791

Root Mean Square Error of Approximation:

RMSEA 0.702

90 Percent Confidence Interval 0.628 0.778

P-value RMSEA <= 0.05 0.000

Standardized Root Mean Square Residual:

SRMR 0.872

Parameter estimates:

Information Expected

Standard Errors Standard

Estimate Std.err Z-value P(>|z|) Std.lv Std.all

Latent variables:

SE =~

RealGDP 1.000 8.246 0.979

LaborForce 0.030 0.245 0.337

M0M1 0.011 0.093 1.005

C =~

GDPperCapita 1.000 14.336 0.005

BribeIndex -0.034 -0.487 -0.981

Judicialind. -0.002 -0.024 -0.058

Regressions:

SE ~

Businessreg -39.952 -4.845 -0.856

UnemplRate 1.276 0.155 0.362

Trans.Subs -8.805 -1.068 -0.316

Govconsump -18.037 -2.187 -0.702

C ~

GovEffect -55.532 -3.873 -0.401

FiscalFree 0.916 0.064 0.303

BeauCosts -4.279 -0.298 -0.449

RuleofLaw 69.165 4.824 0.533

Covariances:

SE ~~

C -78.153 -1.022 -1.022

Variances:

RealGDP 2.878 2.878 0.041

LaborForce 0.468 0.468 0.887

M0M1 -0.000 -0.000 -0.009

GDPperCapita 8466734.775 8466734.775 1.000

BribeIndex 0.009 0.009 0.038

Judicialind. 0.174 0.174 0.997

SE 48.426 0.712 0.712

C 120.722 0.587 0.587

Warning message:

In sqrt(est[rv.idx]) : NaNs produced

Is this reliable??? What does the warning message that I am receiving mean?

Thank you again,

Best

Edward Rigdon

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Nov 30, 2014, 1:13:42 PM11/30/14

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You are estimating 57 free parameters on the strength of 11 cases. No, the results cannot be interpreted.

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Edward Rigdon

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Nov 30, 2014, 1:15:49 PM11/30/14

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You are estimating 57 free parameters on the strength of 11 cases. You should treat the results as a collection of random numbers.

--Ec Rigdon

Sent from my iPad

On Nov 30, 2014, at 11:36 AM, Daca 33 <dem...@gmail.com> wrote:

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