Infinity degrees of freedom and no standard errors when running runMI command

garc...@unlv.nevada.edu

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Jun 28, 2018, 7:07:27 PM6/28/18

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Hello,

I am new to R and am currently working on a project where I am fitting several CFA models to imputed data. I am running into an issue where the output tells me that the model converges. However, when looking closer at the factor loadings I noticed that several of my indicators have "INF" degrees of freedom (which I understand to mean infinity degrees of freedom) while others have no standard errors or p-values calculated. Further, none of the standard errors or p-values for the variances have been calculated. Here is the code that I use to specify and fit the model:

mod.a2 <- 'odd.f =~ odd1sc + odd2sc + odd3sc + odds1sc + odds2sc + odds3sc + odds4sc + odds5sc + odds6sc'

# Fit Model A

fit.mod.a2.wlsmvs.mi <- runMI(model = mod.a2, data = bag.sem, estimator = "WLSMVS", fun = "cfa",

std.lv = TRUE, verbose = TRUE, ordered = c("odd1sc", "odd2sc", "odd3sc", "odds1sc", "odds2sc",

"odds3sc", "odds4sc", "odds5sc", "odds6sc"))

# Summary fit statistics/factor loadings

summary(fit.mod.a2.wlsmvs.mi)

fitmeasures(fit.mod.a2.wlsmvs.mi, fit.measures = "all")

Here is what I see when looking at the output:

Latent Variables:

Estimate Std.Err t-value df P(>|t|)

odd.f =~

odd1sc 0.831 0.020 42.231 Inf 0.000

odd2sc 0.843 0.018 46.194 Inf 0.000

odd3sc 0.789 0.022 35.755 Inf 0.000

odds1sc 0.802 0.021 38.636 865.755 0.000

odds2sc 0.881 0.015 57.411 773.875 0.000

odds3sc 0.681 0.028 24.039 553.293 0.000

odds4sc 0.492 0.037 13.390 758.944 0.000

odds5sc 0.633 0.031 20.623 1076.606 0.000

odds6sc 0.674 0.029 23.585 985.931 0.000

Intercepts:

Estimate Std.Err t-value df P(>|t|)

.odd1sc 0.000

.odd2sc 0.000

.odd3sc 0.000

.odds1sc 0.000

.odds2sc 0.000

.odds3sc 0.000

.odds4sc 0.000

.odds5sc 0.000

.odds6sc 0.000

odd.f 0.000

Thresholds:

Estimate Std.Err t-value df P(>|t|)

odd1sc|t1 -0.710 0.051 -13.909 Inf 0.000

odd1sc|t2 -0.102 0.047 -2.190 Inf 0.029

odd2sc|t1 -0.722 0.051 -14.103 Inf 0.000

odd2sc|t2 -0.027 0.047 -0.581 Inf 0.561

odd3sc|t1 -0.668 0.051 -13.227 Inf 0.000

odd3sc|t2 -0.011 0.047 -0.230 Inf 0.818

odds1sc|t1 -0.636 0.050 -12.695 1664.714 0.000

odds1sc|t2 0.027 0.047 0.579 Inf 0.563

odds2sc|t1 -0.434 0.048 -9.018 2695.879 0.000

odds2sc|t2 0.217 0.047 4.633 Inf 0.000

odds3sc|t1 -0.362 0.048 -7.600 1167.343 0.000

odds3sc|t2 0.344 0.048 7.229 6106.076 0.000

odds4sc|t1 -0.143 0.047 -3.057 1261.238 0.002

odds4sc|t2 0.521 0.049 10.662 2043.255 0.000

odds5sc|t1 -0.541 0.049 -11.011 2409.018 0.000

odds5sc|t2 0.100 0.047 2.149 3309.839 0.032

odds6sc|t1 -0.708 0.051 -13.871 754.554 0.000

odds6sc|t2 -0.013 0.047 -0.282 Inf 0.778

Variances:

Estimate Std.Err t-value df P(>|t|)

.odd1sc 0.309

.odd2sc 0.290

.odd3sc 0.377

.odds1sc 0.356

.odds2sc 0.223

.odds3sc 0.536

.odds4sc 0.758

.odds5sc 0.599

.odds6sc 0.546

odd.f 1.000

Scales y*:

Estimate Std.Err t-value df P(>|t|)

odd1sc 1.000

odd2sc 1.000

odd3sc 1.000

odds1sc 1.000

odds2sc 1.000

odds3sc 1.000

odds4sc 1.000

odds5sc 1.000

odds6sc 1.000

What I think this means is that the model has not fully converged. Is anyone familiar with this problem or able to lend any insight? Again, as a new comer to R, I would be very grateful for any help on this.

Thank you!

Terrence Jorgensen

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Jun 29, 2018, 11:33:24 AM6/29/18

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Is anyone familiar with this problem or able to lend any insight?

There is no problem. The parameters without any SEs or test statistics are not estimated, they are fixed parameters. The infinite df are actually just values > 10000, so I display them as Inf to make the output prettier. This is a new feature -- do you think I should change it (e.g., display ">500")? When the df are over even 200, the t distribution is functionally the normal distribution. Setting the argument asymptotic=TRUE will simply display them as Wald z statistics, like normal lavaan output.

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

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

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

garc...@unlv.nevada.edu

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Jul 23, 2018, 2:34:59 PM7/23/18

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Thank you for your response, Terrence!

I have a follow up question, and please forgive my ignorance as I am new to SEM. Looking at my output, I understand how the scales and intercepts are fixed parameters as they are fixed to either 1 or 0. However, is my variance also a fixed parameter in this case? Those values do not seem to be fixed to me. Though I also understand that my knowledge in this area is modest at best. If you were able to explain this to me, I would greatly appreciate it. Thank you so much!

Terrence Jorgensen

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Jul 24, 2018, 7:38:12 AM7/24/18

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However, is my variance also a fixed parameter in this case? Those values do not seem to be fixed to me.

Yes, they are fixed. Using the default "delta" parameterization, the total variances of the latent item-responses are fixed to be 1, and the residual variances are therefore implied to be 1 minus the variance explained by the factors (or any covariates). Setting paramerization = "theta" will instead fix the residual variances to 1, and implying that the total variance of the latent item-response is 1 plus the explained variances (the "Scales y*" are the square-roots, the total SDs). You can read about these different approaches in: