918 views

Skip to first unread message

Jun 9, 2020, 4:22:39 AM6/9/20

to lavaan

Hi,

__ __

Similar to
this approach described by James Grace (https://prd-wret.s3-us-west-2.amazonaws.com/assets/palladium/production/s3fs-public/atoms/files/SEM_09_1_Modeling_with_latent_variables.pdf), I want to address measurement errors
in my model.

However, my
“eta” is a latent variable described by 3 indicators instead of 1 (in this
example). I want to model the following:

BCol (bill
colour of an individual), being the latent variable defined by nLS, nHS and nCS
(measured and standardized lightness, hue and chroma (saturation); the three axes/parameters that define a colour). The variables themselves are correlated:

nCS &
nLS =0.44

nCS & nHS
= -0.74

nHS & nLS
=0.92

m1, m2 and
m3 are the measurement errors on the observed variables (calculated with ICC
package; repeatability of measurements). Because I want to address the measurement error I added the latent variables
lLS, lHS and lCS between the latent BCol and the measured variables.

My syntax
is the following:

lLS=~nLS

lHS=~nHS

lCS=~nCS

BCol=~lLS+lHS+lCS

nLS ~~
0.05* nLS

nHS~~0.05*nHS

nCS~~0.06*nCS

My output
looks like this:

lavaan 0.6-5 ended normally after 58 iterations

__ __

Estimator ML

Optimization
method NLMINB

Number of free
parameters 9

Number of
observations
598

Model Test User Model:

Test
statistic
0.000

Degrees of
freedom 0

__ __

Parameter Estimates:

__ __

Information Expected

Information
saturated (h1) model Structured

Standard
errors
Standard

__ __

Latent Variables:

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

lLS =~

nLS 1.000 0.974 0.975

lHS =~

nHS 1.000 0.974 0.975

lCS =~

nCS 1.000 0.969 0.969

BCol =~

lLS 1.000 0.758 0.758

lHS 1.680 0.080
21.076 0.000 1.273
1.273

lCS -0.810 0.043
-18.724 0.000 -0.617
-0.617

__ __

Intercepts:

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

.nLS -0.000 0.041
-0.000 1.000 -0.000
-0.000

.nHS -0.000 0.041
-0.000 1.000 -0.000
-0.000

.nCS 0.000 0.041
0.000 1.000 0.000
0.000

.lLS 0.000 0.000 0.000

.lHS 0.000 0.000 0.000

.lCS 0.000 0.000 0.000

BCol 0.000 0.000 0.000

__ __

Variances:

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

.nLS 0.050 0.050 0.050

.nHS 0.050 0.050 0.050

.nCS 0.060 0.060 0.060

.lLS 0.404 0.031
12.943 0.000 0.426
0.426

.lHS -0.589 0.057
-10.359 0.000 -0.621
-0.621

.lCS 0.581 0.039
15.020 0.000 0.619
0.619

BCol 0.545 0.054
10.066 0.000 1.000
1.000

__ __

R-Square:

Estimate

nLS 0.950

nHS 0.950

nCS 0.940

lLS 0.574

lHS NA

lCS 0.381

__ __

I understand that the warning comes from the negative residual covariance in lHS (-0.589) and also results in the standardized estimate being larger than 1 and an NA in the R-square. But what can be the reason for it and what can I do about it. I understand that misspecification of the model can be a reason. The sample size seems ok to me for such a simple model. Can the reason lie in weakness covariance among the indicators? I does not look to me like this because nHS is quite strongly related to the other two variables.

I know that I could fix the variance to zero, but I think that is not what
I am interested in when I want to address measurement errors. Maybe I did not specify
the model correctly?

The
covariance matrix of the latent variables look like this:

lLS lHS
lCS BCol

lLS 0.948

lHS 0.915
0.948

lCS -0.441 -0.741
0.938

BCol 0.545
0.915 -0.441 0.545

I also have
doubts because the model fit seems perfect:

`gfi agfi cfi rni srmr rmsea `

1 1 1 1 0 0

Thanks in
advance for your help!

Jun 9, 2020, 8:35:36 AM6/9/20

to lav...@googlegroups.com

Magali--

1. Your approach is needlessly complicated. The individual factors (ILS, IHS, ICS) add nothing. You could remove them and let the observed variables load on the common factor (BCol) and nothing would change.

2. Your model has 0 DF because it is just-identified. You are estimating 9 parameters (3 observed variable intercepts, 2 loadings, 4 variances or residual variances) from 9 moments of the data (3 observed variable means, 3 variances and 3 covariances). DF = moments of the data - parameters estimated. A model with 0 DF cannot help but fit perfectly in terms of the chi-square and related indicates.

3. The large negative residual variance is a clue that your data are inconsistent with the model. Think about your observed variables--lightness, hue and saturation. Your mdoe says that these three variables all change together, in response to the variable Bill Color. That would mean that Bill Color is really one dimensional--that all Bill Colors can be arranged along one dimension, with lightness, hue and saturation all moving monotonically from less to more or from more to less as you go from one extreme of Bill Color to another.

I don't think that this is what you believe. Rather, Bill Color is the outcome or consequence of lightness, hue and saturation. That is the opposite of a factor model. Instead, that says that Bill Color is a composite of lightness, hue and saturation--

Bill Color = f (lightness, hue, saturation)

I think that the negative residual variance is telling you that, despite the unavoidably perfect fit, the model is wrong for your data.

--Ed Rigdon

.

--

You received this message because you are subscribed to the Google Groups "lavaan" group.

To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/ef680483-e546-43cb-9b53-a2a2c8bdcc47o%40googlegroups.com.

Jun 10, 2020, 10:53:58 AM6/10/20

to lavaan

Hi Edward,

Thanks a
lot for your answer!

I thought
that a latent variable would be appropriate to use as “Bill colour” since two
out of the three correlations were pretty high (0.74 and 0.92). If the
variables are highly correlated I would expect them being arranged on one
dimension. When I run a PCA on the same data I get a PC1 of 80%, which I think
is quiet high. But it is true that the third correlation is much lower (0.44)
and that could indicate that a composite variable might be more useful?! Would
you say that the correlation between the variables can help to give you an idea
if a latent variable or composite variable is more appropriate to use in a
specific case? Of course next to looking at the theoretical background and
hypothesis.

I
understand from literature that a composite variable always needs a response
variable in order to be able to sum the collective effect of all observed
variables. Is that correct? So I could use “individual survival” for instance
as a response variable?

Concerning your first point: I run it again with a different dataset where the model run smoothly (no warnings and good model fit). The latent variable is body size and I added three latents between the observed variable and the latent variable body size to address measurement errors (that are specified/fixed in the model; bold numbers). I run it with once measurement error (variance) fixed at 0.3 for each observed variable and once fixed at 0 (no error) for each observed variable. Even though the path coefficients changes and it is possible to disentangle the effect of the measurement error from the remaining unexplained variation, the latent variable bill size does not change at all in both example.

The easier approach that you suggested, by removing the latent variables (lWL, lTA and lTH) resulted also in exactly the same values for the latent variable. In that model the variance is estimated by the model and not fixed as in the other two examples.

So can I conclude from this that addressing measurement errors is
possible and makes sense in regression analysis (path analysis) but not in a
CFA (models with latent constructs)? Or would it make sense if I add a response
variable (e.g. survival ~ latent body size)?

Thanks!

Magali

Jun 10, 2020, 12:25:31 PM6/10/20

to lav...@googlegroups.com

Magali--

Your first point represents a common misperception, well addressed by a chapter from Karl Joreskog (attached). The common factor model implies, not so much high correlations as proportional correlations. If two observed variables load only on the same common factor, then the ratio of their correlations to any third observed variable must be constant (within sampling variance), across all other variables in the model. With few observed variables in the model, one cannot observe whether or not such proportionality constraints hold.

You could use another variable to If you have other observed variables--whether the are believed to load on the same common factor or not--you could see whether the proportionality constraints implied by the factor model seem to hold.

Whether or not you can "account for measurement error" in any circumstance depends on what you mean by "measurement error."

The difference between the models with an without the extra layer of common factors is cosmetic. If you want your output to include these representations, then keep the extra layer. But you could always reconstruct by hand the same results from a model without the extra layer, or even use the lavaan package's ability to define novel parameters to get the package to calculate those for you, along with standard errors.

I like simple models because they are easier to explain and diagnose.

This list relates to the lavaan package for estimating common factor-based models, but i will answer your other questions briefly.

If you wanted to build a composite-based model, and if you wanted to estimate "optimal" weights, then yes, you need some criterion against which to assess that optimality. If you have a priori estimates of the "measurement error" associated with each observed variable, you could assign weights to the observed variables relative to that, giving higher weight to the observed variables less affected by "measurement error." Exact values of the weights are not generally useful. Rather, it is the relative weights that define the composite.

--Ed Rigdon

--

You received this message because you are subscribed to the Google Groups "lavaan" group.

To unsubscribe from this group and stop receiving emails from it, send an email to lavaan+un...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/lavaan/225532ef-9c87-4e0d-93fa-c16f95ba47abo%40googlegroups.com.

Message has been deleted

Message has been deleted

Jun 12, 2020, 5:03:59 AM6/12/20

to lavaan

Hi Edward,

Thanks a lot for all your answers. It helped me a lot!

Best,

Magali

Reply all

Reply to author

Forward

0 new messages

Search

Clear search

Close search

Google apps

Main menu