CFA - clustered standard errors
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Aaron Charlton
Nov 3, 2015, 6:56:06 PM11/3/15
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I am doing a scale development project with Lavaan. I ran a CFA, but the problem is that I have 43 individuals answer the same questions four times, once for each set of stimuli. Is there a way I can account for this in Lavaan? I was told that I need to "cluster the standard errors", clustering together each individual's response. Does anyone know how to do that? Also, should I use the grouping aspect of the cfa function? Thanks. -Aaron
## confirmatory factor analysis
library(lavaan)
model1 <- ' history =~ HIS1 + HIS2 + HIS3 + HIS4
motivation =~ MOT1 + MOT2 + MOT3 + MOT4
emotion =~ EMO1 + EMO2 + EMO3 + EMO4
fit =~ FIT1 + FIT2 + FIT3 + FIT4 + FIT5'
fit2 <- cfa(model1, data=study1)
Stas Kolenikov
Nov 3, 2015, 10:25:32 PM11/3/15
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Probably something like
library(survey) # thanks to Thomas Lumley
library(lavaan.survey) # thanks to Daniel Oberski
person.as.cluster <- svydesign(ids=~person, probs~=1, data=study1)fit2.clustered <- lavaan.survey(fit2, person.as.cluster, estimator="MLM")
assuming that your data are in semi-long format with each row representing one (out of the four) observations.
Alternatively, you could consider recasting your model as MTMM with the multiple methods being the multiple occasions if you think that the individuals learn in about the same way.
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Education Officer, Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
--
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Aaron Charlton
Nov 4, 2015, 4:47:18 PM11/4/15
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Stas,
Thank you so much for the response. I have actually been trying to use this package, but every time I run the lavann.survey function, I get this error message:
Warning message:
'lavaan::duplicationMatrix' is deprecated.
Use 'lav_matrix_duplication' instead.
See help("Deprecated") and help("lavaan-deprecated").
Following the error message, it fails to do any clustering. Any ideas why this might be happening? Thanks.
Stas Kolenikov
Nov 4, 2015, 5:17:20 PM11/4/15
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That would be a question to Daniel Oberski, and something for him to fix. (Duplication matrices are used to convert different vectorizations of a symmetric matrix, and that's something you have to process when dealing with the moment matrices.)
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Education Officer, Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
--
yrosseel
Nov 5, 2015, 3:04:20 AM11/5/15
to lav...@googlegroups.com
On 11/04/2015 10:47 PM, Aaron Charlton wrote:
> Warning message:
> 'lavaan::duplicationMatrix' is deprecated.
> Use 'lav_matrix_duplication' instead.
> See help("Deprecated") and help("lavaan-deprecated").
This is a (completely harmless) warning message, not an error!
> Warning message:
> 'lavaan::duplicationMatrix' is deprecated.
> Use 'lav_matrix_duplication' instead.
> See help("Deprecated") and help("lavaan-deprecated").
> Following the error message, it fails to do any clustering.
converge? Please show us the complete R script and the output, and we
may be able help you better.
Yves.
Aaron Charlton
Nov 5, 2015, 2:06:03 PM11/5/15
to lavaan
I seem to get exactly the same model with and without clustering.
Here is my code:
> str(study1)
'data.frame': 176 obs. of 21 variables:
$ ID : chr "951138372" "951138372" "951138372" "951138372" ...
$ stimulus: Factor w/ 4 levels "adidas_wc","mcD_olymp",..: 1 2 4 3 1 2 4 3 1 2 ...
$ HIS1 : int 7 5 5 6 7 3 2 2 7 6 ...
$ HIS2 : int 6 3 3 5 7 3 2 2 7 6 ...
$ HIS3 : int 6 5 5 5 7 3 2 2 7 7 ...
$ HIS4 : int 6 3 2 5 7 3 2 2 7 4 ...
$ MOT1 : int 6 5 6 6 7 3 3 6 7 4 ...
$ MOT2 : int 7 7 6 7 7 3 3 5 7 7 ...
$ MOT3 : int 5 5 5 5 1 5 3 3 4 4 ...
$ MOT4 : int 6 6 6 6 7 3 5 5 7 5 ...
$ EMO1 : int 6 5 5 5 7 2 3 3 7 2 ...
$ EMO2 : int 6 5 5 5 7 2 4 3 5 4 ...
$ EMO3 : int 5 6 6 5 7 4 3 3 5 6 ...
$ EMO4 : int 6 5 5 5 7 3 3 4 7 6 ...
$ FIT1 : int 7 2 2 6 7 2 3 3 7 1 ...
$ FIT2 : int 7 2 2 6 7 2 3 3 7 1 ...
$ FIT3 : int 7 2 2 7 7 2 3 4 7 3 ...
$ FIT4 : int 6 3 3 5 7 2 3 3 7 1 ...
$ FIT5 : int 7 2 2 6 7 2 3 4 7 1 ...
$ OUT1 : int 6 3 3 6 7 2 3 5 7 4 ...
$ OUT2 : int 7 7 2 5 5 3 3 4 7 7 ...
> ## confirmatory factor analysis
> library(lavaan)
> model1 <- ' history =~ HIS1 + HIS2 + HIS3 + HIS4
+ motivation =~ MOT1 + MOT2 + MOT3 + MOT4
+ emotion =~ EMO1 + EMO2 + EMO3 + EMO4'
> # fit =~ FIT1 + FIT2 + FIT3 + FIT4 + FIT5'
> fit2 <- cfa(model1, data=study1)
> library(survey)
> library(lavaan.survey)
> person.as.cluster <- svydesign(ids=~ID, probs=~1, data=study1)
> fit2.clustered <- lavaan.survey(fit2, person.as.cluster, estimator="MLM")
Warning message:
'lavaan::duplicationMatrix' is deprecated.
Use 'lav_matrix_duplication' instead.
See help("Deprecated") and help("lavaan-deprecated").
> summary(fit2)
lavaan (0.5-19) converged normally after 41 iterations
Number of observations 176
Estimator ML
Minimum Function Test Statistic 212.844
Degrees of freedom 51
P-value (Chi-square) 0.000
Parameter Estimates:
Information Expected
Standard Errors Standard
Latent Variables:
Estimate Std.Err Z-value P(>|z|)
history =~
HIS1 1.000
HIS2 0.952 0.034 28.164 0.000
HIS3 0.962 0.034 28.420 0.000
HIS4 0.902 0.039 22.969 0.000
motivation =~
MOT1 1.000
MOT2 0.603 0.059 10.215 0.000
MOT3 -0.346 0.093 -3.722 0.000
MOT4 0.697 0.054 12.815 0.000
emotion =~
EMO1 1.000
EMO2 1.054 0.066 15.970 0.000
EMO3 -0.410 0.078 -5.230 0.000
EMO4 0.771 0.071 10.887 0.000
Covariances:
Estimate Std.Err Z-value P(>|z|)
history ~~
motivation 1.382 0.205 6.755 0.000
emotion 1.313 0.200 6.553 0.000
motivation ~~
emotion 1.575 0.209 7.525 0.000
Variances:
Estimate Std.Err Z-value P(>|z|)
HIS1 0.121 0.029 4.122 0.000
HIS2 0.338 0.045 7.548 0.000
HIS3 0.337 0.045 7.492 0.000
HIS4 0.520 0.062 8.369 0.000
MOT1 0.674 0.101 6.701 0.000
MOT2 0.650 0.077 8.432 0.000
MOT3 2.218 0.239 9.292 0.000
MOT4 0.404 0.056 7.255 0.000
EMO1 0.625 0.089 6.995 0.000
EMO2 0.377 0.074 5.078 0.000
EMO3 1.614 0.175 9.238 0.000
EMO4 1.002 0.117 8.547 0.000
history 2.409 0.271 8.900 0.000
motivation 1.681 0.251 6.708 0.000
emotion 1.737 0.250 6.948 0.000
> summary(fit2.clustered)
lavaan (0.5-19) converged normally after 41 iterations
Number of observations 176
Estimator ML Robust
Minimum Function Test Statistic 212.844 138.145
Degrees of freedom 51 51
P-value (Chi-square) 0.000 0.000
Scaling correction factor 1.541
for the Satorra-Bentler correction
Parameter Estimates:
Information Expected
Standard Errors Robust.sem
Latent Variables:
Estimate Std.Err Z-value P(>|z|)
history =~
HIS1 1.000
HIS2 0.952 0.024 39.953 0.000
HIS3 0.962 0.027 35.710 0.000
HIS4 0.902 0.033 27.354 0.000
motivation =~
MOT1 1.000
MOT2 0.603 0.078 7.781 0.000
MOT3 -0.346 0.169 -2.044 0.041
MOT4 0.697 0.053 13.116 0.000
emotion =~
EMO1 1.000
EMO2 1.054 0.054 19.382 0.000
EMO3 -0.410 0.139 -2.956 0.003
EMO4 0.771 0.078 9.941 0.000
Covariances:
Estimate Std.Err Z-value P(>|z|)
history ~~
motivation 1.382 0.246 5.614 0.000
emotion 1.313 0.199 6.586 0.000
motivation ~~
emotion 1.575 0.213 7.395 0.000
Intercepts:
Estimate Std.Err Z-value P(>|z|)
HIS1 4.438 0.132 33.497 0.000
HIS2 4.278 0.142 30.192 0.000
HIS3 4.517 0.128 35.302 0.000
HIS4 4.205 0.128 32.868 0.000
MOT1 4.642 0.126 36.806 0.000
MOT2 5.608 0.112 50.256 0.000
MOT3 4.085 0.185 22.085 0.000
MOT4 5.188 0.103 50.450 0.000
EMO1 4.614 0.104 44.270 0.000
EMO2 4.710 0.134 35.235 0.000
EMO3 4.438 0.116 38.386 0.000
EMO4 4.506 0.113 39.945 0.000
history 0.000
motivation 0.000
emotion 0.000
Variances:
Estimate Std.Err Z-value P(>|z|)
HIS1 0.121 0.039 3.099 0.002
HIS2 0.338 0.123 2.735 0.006
HIS3 0.337 0.060 5.636 0.000
HIS4 0.520 0.099 5.238 0.000
MOT1 0.674 0.128 5.271 0.000
MOT2 0.650 0.093 6.999 0.000
MOT3 2.218 0.359 6.184 0.000
MOT4 0.404 0.067 6.074 0.000
EMO1 0.625 0.150 4.155 0.000
EMO2 0.377 0.094 4.007 0.000
EMO3 1.614 0.235 6.855 0.000
EMO4 1.002 0.223 4.499 0.000
history 2.409 0.246 9.785 0.000
motivation 1.681 0.273 6.159 0.000
emotion 1.737 0.266 6.527 0.000
> library(semTools)
> reliability(fit2)
history motivation emotion total
alpha 0.9634943 0.3767812 0.4649107 0.8679822
omega 0.9638765 0.6193784 0.7369433 0.9261453
omega2 0.9638765 0.6193784 0.7369433 0.9261453
omega3 0.9637533 0.6348940 0.7667986 0.8763399
avevar 0.8697854 0.4561635 0.5797538 0.6580224
> reliability(fit2.clustered)
history motivation emotion total
alpha 0.9634943 0.3767812 0.4649107 0.8679822
omega 0.9638765 0.6193784 0.7369433 0.9261453
omega2 0.9638765 0.6193784 0.7369433 0.9261453
omega3 0.9637533 0.6348940 0.7667986 0.8763399
avevar 0.8697854 0.4561635 0.5797538 0.6580224
>
Stas Kolenikov
Nov 5, 2015, 3:44:35 PM11/5/15
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So are HIS1, HIS2, HIS3, HIS4 your four occasions? If they are, and each individual is just one line of the data, then you don't have anything to cluster for. If you had scales administered four times, and you wanted to build a model where the latent construct is your latent variable, and items are the observed variables, then the idea of clustering could have been entertained to model the dependencies between the four occasions over time. As it stands, however, you have a CFA with no structure imposed; a very reasonable question to ask is whether you have measurement invariance between the occasions -- but it looks like motivation and emotion will likely fail that due to something odd happening on the third occasion.
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Education Officer, Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
--
Aaron Charlton
Nov 5, 2015, 4:12:44 PM11/5/15
to lavaan
Hi, Stas.
Not exactly. HIS1-HIS4 are four different scale items that hopefully measure the latent variable 'history'. My occasions are contained in the 'stimulus' variable, a factor with four levels. I have the data in long form, so there are 4 observations for each person (ID) -- one for each of the four stimuli. Thanks. -Aaron
Stas Kolenikov
Nov 5, 2015, 4:16:40 PM11/5/15
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Oh I see. Well your models aren't exactly the same with and without clustering. With clustering, the standard errors are different (as they should be; the point estimates should be the same). Also, with clustering, you should forget about the MLM fit test statistic reported (the 212 number), and only look at the "robust" statistic reported (the 138 number).
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Education Officer, Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
Aaron Charlton
Nov 5, 2015, 4:26:52 PM11/5/15
to lavaan
Stas,
Thanks! Is there a resource you would recommend on interpreting the clustered output? -Aaron
Stas Kolenikov
Nov 5, 2015, 5:57:32 PM11/5/15
to lav...@googlegroups.com
-- Stas Kolenikov, PhD, PStat (ASA, SSC)
-- Principal Survey Scientist, Abt SRBI
-- Education Officer, Survey Research Methods Section of the American Statistical Association
-- Opinions stated in this email are mine only, and do not reflect the position of my employer
-- http://stas.kolenikov.name
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