# Estimated LV variances negative for first order factor (with two factors predicting a second order factor)

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### Danushika Sivanathan

Jun 29, 2020, 12:02:04 AM6/29/20
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Hi All,

This may seem similar to other issues. I have read up on https://groups.google.com/forum/#!msg/lavaan/SYTgS8EfnLg/13aIN8xoAQAJ but didn't seem to help so I decided to make a new post. My model is the following:

Model = CSW =~ x1:x7
LED =~ x8:x14
GF =~ x14: x21
VAN =~ x22:x28
HN=~ x29:x33
GN =~ a*VAN + a*LED
VN =~ CSW + GF + HN

When I run this model I get the error stating some of the estimated latent variances are negative and it is for the factor VAN. So I fixed the error variance to equal to 0.01 and found the factor loads onto GN at 0.99. I then tried with GN and VN not being correlated and found the loading to decrease to 0.948. Normally, GN and VN correlate at around 0.4-0.5.

I also tried running LED and VAN as one factor but ended up with really poor model fit indices. When I run just the part of the model that involves GN I get a loading of 0.87 for VAN onto GN. I am not super familiar with the mathematics of this so I don't really understand what is going on. I thought maybe it was due to items from LED/VAN that were also loading highly onto the other factor, but modification indices quickly showed that was not the case. Currently, my next option is to explore model building to see where this issue might lie. But before I launch into that I wanted to see if you guys had any ideas.

For more contextual information LED only really correlates with VAN and none of the other factors (expected theoretically). The two LED and VAN factors make theoretical and we would expect to observe those.

My questions with this are:
1. Is it a problem to have a factor load at > 0.80 onto a second order factor, when there are only two manifest factors?
2. What are options around this error?
I really appreciate any feedback! Thank you
Danu

### Terrence Jorgensen

Jun 30, 2020, 6:09:24 PM6/30/20
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Model = CSW =~ x1:x7
LED =~ x8:x14
GF =~ x14: x21
VAN =~ x22:x28
HN=~ x29:x33
GN =~ a*VAN + a*LED
VN =~ CSW + GF + HN

Your model syntax is not wrapped in quotation marks to make it a character string.  Furthermore, you seem to be trying some kind of shortcut that does not exist.  The colon operator specifies a product between 2 variables, so CSW =~ x1:x7 is specifying a single-indicator factor (indicator is x1 times x7), not a factor with 7 indicators.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

Message has been deleted

### Danushika Sivanathan

Jun 30, 2020, 8:53:20 PM6/30/20
to lavaan
Hi Terence,

That is my mistake. I used the colon as a short hand. But the actual model is below:

mode = '
CSW =~ CSW_1 + CSW_2 + CSW_3 + CSW_4 + CSW_5 + CSW_6 + CSW_7
LED =~ LED_1 + LED_3 + LED_4 + LED_5 + LED_6 + LED_9 + LED_10
GF =~ GF_1 + GF_2 + GF_3 + GF_4 + GF_5 + GF_6 + GF_8
VAN =~ VAN_2 + VAN_3 + VAN_4 + VAN_5 + VAN_6 + VAN_7
HN =~ HN_1 + HN_2 + HN_3 + HN_4 + HN_5
VN =~ CSW + GF + HN
GN =~ a*LED + a*VAN
VAN_2 ~~ VAN_3
'

I allowed the two items to correlate with each other due to similar item content. The items are scored on a 6 point Likert scale and I had a sample size of 501. I did run the analyses on the whole sample (N = 1003) to ensure it was not a sample size problem and found the same challenges as I mentioned in my post.

Any help would be so appreciated.

Cheers,
Danu