Two-level CFA and restriction of error variance of the between level

janmicha...@googlemail.com

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Feb 7, 2019, 7:04:18 AM2/7/19

to lavaan

I'm wondering why it could make sense to restrict the error variance at the between level in a two-level CFA (or SEM)?

This is done in Example 9.6 in the MPLUS manual and also repeated (marked as optional) in a slide-deck by Yves Rosseel on Multilevel Structural Equation Modeling with lavaan.

I'm using lavaan and I was wondering when this could make sense and what it implies?

I sometimes get negative error variances at the between level (i.e., Haywood cases) so a qualified constraint would be useful for me, but I don't want to do it without understanding its origin.

I'm having data on 15 items that I suppose belong to 3 factors and 20 clusters with about 2000 observations (distributed more or less balanced across the cluster, but not equally).

Chandra Sekhar Singh

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Feb 7, 2019, 7:47:44 AM2/7/19

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Hi.

I need MPLUS software for my PhD data analysis.

I am using Multi-level modeling in my research. pls, help in this regard.

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Best regards,

Chandra Sekhar Singh
PhD Scholar (Management)
ABV-Indian Institute of Information Technology & Management, Gwalior, M.P. India (Institute of National Importance)
Contact No. +91-9425718177

janmicha...@googlemail.com

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Feb 7, 2019, 10:46:14 AM2/7/19

to lavaan

maybe to add on my current model: The error variances in the between level model are extremely small:

Variances:

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

.x1 0.001 0.001 0.789 0.430

.x2 -0.001 0.001 -0.921 0.357

.x3 -0.002 0.001 -2.772 0.006

.x4 0.000 0.001 0.041 0.967

.x5 -0.000 0.001 -0.590 0.555

.x6 -0.000 0.001 -0.117 0.907

.x7 0.001 0.001 0.623 0.533

.x8 -0.001 0.001 -1.572 0.116

.x9 0.000 0.001 0.314 0.754

.x10 -0.000 0.001 -0.383 0.702

.x11 -0.001 0.000 -2.440 0.015

.x12 -0.001 0.000 -2.265 0.024

.x13 0.001 0.001 0.764 0.445

.x14 -0.001 0.001 -1.532 0.125

.x15 -0.000 0.000 -1.228 0.219

Terrence Jorgensen

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Feb 8, 2019, 6:37:24 AM2/8/19

to lavaan

I sometimes get negative error variances at the between level (i.e., Haywood cases) so a qualified constraint would be useful for me, but I don't want to do it without understanding its origin.

If your items meet scalar ("strong") invariance across clusters, that implies residual variances == 0 at the between level.

https://www.frontiersin.org/articles/10.3389/fpsyg.2017.01640/full

Most of the estimates do not significantly differ from 0 (the one exception might be a Type I error: 1 out of 15 tests would not be a surprise).

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

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

http://www.uva.nl/profile/t.d.jorgensen

janmicha...@googlemail.com

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Feb 9, 2019, 8:50:19 AM2/9/19

to lavaan

Thank you for your excellent reference. I very much enjoyed reading it. The link between multi-level SEM and multi-group SEM was actually the one that solved my questions.

I indeed have strong / scalar invariance in the multi-group setting.

Chao Xu

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Feb 9, 2019, 9:01:38 PM2/9/19

to lavaan

Hi,

I have an issue that, if the error variance at the between level is not constrained to 0, my model become non-identifiable. What problem could this be due to? Would it be possible for you to share your model syntax? Thank you very much.

Chao Xu

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Feb 10, 2019, 4:37:20 PM2/10/19

to lavaan

I found the source of the problem by relaxing the between-level residual variance constraints one by one. Only 3 out of 40 items are problematic and cause non-convergence.