CFA, invariance, correlated uniqueness and df

[19lucy...@gmail.com]

Hi everyone!

I am running a CFA and testing for invariance using lavaan.

My model consists of three subscales, one of 3 items and two of two items each. The scales have been measured twice.

I am new to R and lavaan and therefore I did not used the commands offered by lavaan  to understand what actually is going on.

So far as I know there are two ways "measuring" the scale of the LV:

Either by fixing the mean=0 and variance=1 of the LV

or by setting the first items' factor loadings to 1 and the intercept to 0.

Therefore I have two different models:

Model1 <- '

LV1_1 =~ NA*Item1+ alambda21*Item2 + alambda31*Item 3

LV1_2 =~ NA*Item1+ alambda22*Item2 + alambda32*Item3

LV2_1 =~ NA*Item4 + blambda21*Item5

LV2_2 =~ NA*Item4* blambda22*Item5

LV3_1 =~ NA*Item6 + clambda21*Item7

LV3_2 =~ NA*Item6 + clambda22*Item7

#autocorrelation#

Item1_1~~Item1_2

Item2_1~~Item2_2

Item3_1~~Item3_2

Item4_1~~Item4_2

Item5_1~~Item5_2

Item6_1~~Item6_2

Item7_1~~Item7_2

#Variance LV

LV1_1~~1*LV1_1

LV1_2~~1*LV1_2

LV2_1~~1*LV2_1

LV2_2~~1*LV2_2

LV3_1~~1*LV3_1

LV3_2~~1*LV3_2

#Variance means

LV1_1 ~ 0*1

LV1_2 ~ 0*1

LV2_1 ~ 0*1

LV2_2 ~0*1

LV3_1~0*1

LV3_2~0*1

'

Model1.fit <- sem(Model1,data = data1_2, estimator = "mlr", missing = "fiml")

Model2 <- '

LV1_1 =~ 1*Item1+ alambda21*Item2 + alambda31*Item 3

LV1_2 =~ 1*Item1+ alambda22*Item2 + alambda32*Item3

LV2_1 =~ 1*Item4 + blambda21*Item5

LV2_2 =~ 1*Item4* blambda22*Item5

LV3_1 =~ 1*Item6 + clambda21*Item7

LV3_2 =~ 1*Item6 + clambda22*Item7

#autocorrelation#

Item1_1~~Item1_2

Item2_1~~Item2_2

Item3_1~~Item3_2

Item4_1~~Item4_2

Item5_1~~Item5_2

Item6_1~~Item6_2

Item7_1~~Item7_2

#Intercepts#

Item1_1~ 0*1

Item2_1~ 0*1

Item3_1~ 0*1

Item4_1~ 0*1

Item5_1~ 0*1

Item6_1~ 0*1

Item7_1~ 0*1

#Variance LV

LV1_1~~1*LV1_1

LV1_2~~1*LV1_2

LV2_1~~1*LV2_1

LV2_2~~1*LV2_2

LV3_1~~1*LV3_1

LV3_2~~1*LV3_2

#Variance means

LV1_1 ~ 0*1

LV1_2 ~ 0*1

LV2_1 ~ 0*1

LV2_2 ~0*1

LV3_1~0*1

LV3_2~0*1

'

Model2.fit <- sem(Model2,data = data1_2, estimator = "mlr", missing = "fiml")

My questions are the following ones:

Do I need to estimate the covariances between the LV's and using the command " orthogonal=F"? It's working without problems however I wonder if it's important for future measurements.

My second questions is: When I don't calculate the correlated uniqueness, why don't my dfs change in this model?

Because when I measure weak, strong and strict invariance there is a difference in the dfs, depending on whether I calculated correlated uniqueness or not.

Moreover measuring the other stages of invariance produces different dfs for the two different models.

For example for weak invariance:

62 when fixing the mean and variance and 59 when fixing the first factor loadings to 1.

And for strict invariance:

69 for model 1 and 63 for model 2.

When I look at the scales separately the differences are even bigger.

And what I really don't understand:

the df's differ between the LV2 and Lv3 scale even both consists of two items.

I am really happy about any comment or idea that can help me understanding what's going on.

Thank you!

Lucy

[Terrence Jorgensen]

Do I need to estimate the covariances between the LV's and using the command " orthogonal=F"?

No, that is the default

lavOptions("orthogonal")

When I don't calculate the correlated uniqueness, why don't my dfs change in this model?

Because when I measure weak, strong and strict invariance there is a difference in the dfs, depending on whether I calculated correlated uniqueness or not.

It is unclear what model(s) you are talking about comparing.  But some mistakes in your syntax could lead to unexpected results.  When you fixed the first intercepts to 0:

• you only did so for Time 1, not Time 2
• you forgot to free the latent means (confusingly labeled "variance means" in the syntax)

Likewise, when you fixed the first loadings to 1, you forgot to free the latent variances.

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