Ordinal variables in lavaan: Difference between ordered=TRUE and estimator=DWLS

Linda Michelle

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May 11, 2021, 5:33:47 AM5/11/21

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Hello everyone,

I am applying SEM using Lavaan on a dataset with ordinal variables.

I read online that I should use the DWLS estimator for this.

I have tried two different ways of getting the results:

1) sem(sem(MyModel, MyData, ordered=TRUE)

2) sem(MyModel,MyData,estimator="DWLS")

In both cases, the DWLS estimator is used with optimisation method NLMINB.

However, the parameters and goodness-of-fit measures are completely different for both outputs.

Does anyone know what the difference is between these two methods and which one I should use?

Rick Hass

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May 13, 2021, 9:57:20 AM5/13/21

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Hi,

I think your answer may be down the bottom here: https://lavaan.ugent.be/tutorial/cat.html

Such that in specifying order = TRUE, you're getting the mean and variance adjusted test statistic and the full weight matrix (rather than diagonalized) is used for the parameter estimates. When specifying DWLS, without the ordered argument, those two things down happen, thus different fit measures (fit function) and different parameter estimates.

As far as what to use, that's your choice! If you want to truly model the indicators as ordinal, I'd go with ordered = TRUE.

-R

Saeed Abbas Shah

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Dec 12, 2021, 2:04:05 PM12/12/21

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Hi,

Did you find the answer to your question because I am also facing same problem?

If you know, kindly share your learning.

Thanks

Regards

Chesnut, Ryan

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Dec 12, 2021, 3:04:26 PM12/12/21

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In the second instance, it doesn’t look like any variables are declared ordered, so lavaan is using the DWLS estimator but treating the data as continuous. If you have ordered data, the first option would be preferable because it tells lavaan to treat the data as ordered.

Sent from my iPhone

On Dec 12, 2021, at 2:04 PM, Saeed Abbas Shah <s.a...@iba-suk.edu.pk> wrote:

Hi,

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Shu Fai Cheung

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Dec 12, 2021, 10:13:05 PM12/12/21

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I am not contributing any new information. Just share two examples to illustrate others' responses:

library(lavaan)
#> This is lavaan 0.6-9
#> lavaan is FREE software! Please report any bugs.
# Round the indicator scores
vnames <- paste0("x", 1:6)
HolzingerSwineford1939[, vnames] <- round(HolzingerSwineford1939[, vnames])
lapply(HolzingerSwineford1939[, vnames], table)
#> $x1
#>
#> 1 2 3 4 5 6 7 8
#> 1 4 27 73 92 84 16 4
#>
#> $x2
#>
#> 2 4 5 6 7 8 9
#> 1 17 72 127 39 36 9
#>
#> $x3
#>
#> 0 1 2 3 4
#> 11 73 113 46 58
#>
#> $x4
#>
#> 0 1 2 3 4 5 6
#> 3 20 60 127 56 25 10
#>
#> $x5
#>
#> 1 2 3 4 5 6 7
#> 3 30 42 89 62 72 3
#>
#> $x6
#>
#> 0 1 2 3 4 5 6
#> 6 79 117 65 20 11 3
# Fit a CFA model
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6'

# "ordered" only
fit1 <- cfa(HS.model, data = HolzingerSwineford1939, ordered = TRUE)
summary(fit1)
#> lavaan 0.6-9 ended normally after 18 iterations
#>
#> Estimator DWLS
#> Optimization method NLMINB
#> Number of model parameters 42
#>
#> Number of observations 301
#>
#> Model Test User Model:
#> Standard Robust
#> Test Statistic 11.546 19.813
#> Degrees of freedom 8 8
#> P-value (Chi-square) 0.173 0.011
#> Scaling correction factor 0.625
#> Shift parameter 1.336
#> simple second-order correction
#>
#> Parameter Estimates:
#>
#> Standard errors Robust.sem
#> Information Expected
#> Information saturated (h1) model Unstructured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> visual =~
#> x1 1.000
#> x2 0.461 0.089 5.180 0.000
#> x3 0.613 0.105 5.837 0.000
#> textual =~
#> x4 1.000
#> x5 1.022 0.047 21.578 0.000
#> x6 0.989 0.042 23.351 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> visual ~~
#> textual 0.326 0.044 7.349 0.000
#>
#> Intercepts:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.000
#> .x2 0.000
#> .x3 0.000
#> .x4 0.000
#> .x5 0.000
#> .x6 0.000
#> visual 0.000
#> textual 0.000
#>
#> Thresholds:
#> Estimate Std.Err z-value P(>|z|)
#> x1|t1 -2.714 0.331 -8.193 0.000
#> x1|t2 -2.129 0.179 -11.928 0.000
#> x1|t3 -1.246 0.097 -12.850 0.000
#> x1|t4 -0.388 0.074 -5.223 0.000
#> x1|t5 0.397 0.074 5.337 0.000
#> x1|t6 1.503 0.111 13.479 0.000
#> x1|t7 2.218 0.194 11.444 0.000
#> x2|t1 -2.714 0.331 -8.193 0.000
#> x2|t2 -1.556 0.115 -13.508 0.000
#> x2|t3 -0.527 0.076 -6.925 0.000
#> x2|t4 0.586 0.077 7.600 0.000
#> x2|t5 1.039 0.088 11.736 0.000
#> x2|t6 1.882 0.145 12.989 0.000
#> x3|t1 -1.792 0.135 -13.244 0.000
#> x3|t2 -0.586 0.077 -7.600 0.000
#> x3|t3 0.397 0.074 5.337 0.000
#> x3|t4 0.868 0.083 10.434 0.000
#> x4|t1 -2.328 0.216 -10.785 0.000
#> x4|t2 -1.430 0.107 -13.383 0.000
#> x4|t3 -0.596 0.077 -7.712 0.000
#> x4|t4 0.518 0.076 6.812 0.000
#> x4|t5 1.194 0.095 12.619 0.000
#> x4|t6 1.835 0.140 13.131 0.000
#> x5|t1 -2.328 0.216 -10.785 0.000
#> x5|t2 -1.228 0.096 -12.775 0.000
#> x5|t3 -0.677 0.079 -8.601 0.000
#> x5|t4 0.113 0.073 1.553 0.120
#> x5|t5 0.677 0.079 8.601 0.000
#> x5|t6 2.328 0.216 10.785 0.000
#> x6|t1 -2.055 0.167 -12.296 0.000
#> x6|t2 -0.576 0.077 -7.488 0.000
#> x6|t3 0.443 0.075 5.906 0.000
#> x6|t4 1.211 0.095 12.698 0.000
#> x6|t5 1.680 0.125 13.447 0.000
#> x6|t6 2.328 0.216 10.785 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.222
#> .x2 0.834
#> .x3 0.708
#> .x4 0.266
#> .x5 0.234
#> .x6 0.283
#> visual 0.778 0.145 5.371 0.000
#> textual 0.734 0.046 15.967 0.000
#>
#> Scales y*:
#> Estimate Std.Err z-value P(>|z|)
#> x1 1.000
#> x2 1.000
#> x3 1.000
#> x4 1.000
#> x5 1.000
#> x6 1.000
lavInspect(fit1, "ordered")
#> [1] "x1" "x2" "x3" "x4" "x5" "x6"
# "DWLS" only
fit2 <- cfa(HS.model, data = HolzingerSwineford1939, estimator = "DWLS")
summary(fit2)
#> lavaan 0.6-9 ended normally after 36 iterations
#>
#> Estimator DWLS
#> Optimization method NLMINB
#> Number of model parameters 13
#>
#> Number of observations 301
#>
#> Model Test User Model:
#>
#> Test statistic 8.480
#> Degrees of freedom 8
#> P-value (Chi-square) 0.388
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Unstructured
#>
#> Latent Variables:
#> Estimate Std.Err z-value P(>|z|)
#> visual =~
#> x1 1.000
#> x2 0.457 0.090 5.051 0.000
#> x3 0.571 0.105 5.452 0.000
#> textual =~
#> x4 1.000
#> x5 1.050 0.124 8.484 0.000
#> x6 0.952 0.110 8.664 0.000
#>
#> Covariances:
#> Estimate Std.Err z-value P(>|z|)
#> visual ~~
#> textual 0.422 0.056 7.605 0.000
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .x1 0.382 0.241 1.585 0.113
#> .x2 1.182 0.133 8.859 0.000
#> .x3 0.939 0.109 8.639 0.000
#> .x4 0.386 0.188 2.049 0.040
#> .x5 0.683 0.197 3.470 0.001
#> .x6 0.388 0.180 2.150 0.032
#> visual 1.005 0.213 4.715 0.000
#> textual 0.983 0.146 6.717 0.000
lavInspect(fit2, "ordered")
#> character(0)

In the first example (fit1), the argument order is used. It will automatically compute the tetrachoric or polychoric correlations for ordinal variables, add thresholds and the mean structure to the model, use DWLS as the estimator, set standard error to "robust.sem", and report robust fit measures.

In the second example (fit2), only estimator = "DWLS" is used. lavaan will do only what is instructed: setting the estimator to "DWLS". lavInspect() result confirms that no variables are treated as ordinal.

Therefore, just use order (set it to TRUE, or specify the ordinal variables if only some of them are ordinal). It will configure other arguments accordingly. Do not manually set those related arguments unless you do want to override the default options for ordinal variables.