difference between mplus and lavaan thresholds

[merm.m...@gmail.com]

Both Mplus and Lavaan produce the same estimated sample threshold statistics.  However, when conducting an sem model, why is it that Mplus uses different thresholds than Lavaan in the actual model?  Mplus uses different threshold estimates than Lavaan does in the actual model when estimating factor loadings or variances.

Thanks.

[yrosseel]

I'm not sure what you mean. Can you provide an example?

Yves.

[merm.m...@gmail.com]

Mplus starting threshold estimates = lavaan's final thresholds estimates.

Mplus starting thresholds:

STARTING VALUES

           TAU

              I1$1          I1$2          I1$3          I2$1          I2$2

              ________      ________      ________      ________      ________

      1        -2.394        -1.001         1.282        -2.394        -1.036

           TAU

              I2$3          I3$1          I3$2          I3$3          I4$1

              ________      ________      ________      ________      ________

      1         0.812        -2.394        -0.648         1.073        -1.111

           TAU

              I4$2          I5$1          I5$2          I6$1          I6$2

              ________      ________      ________      ________      ________

      1         1.192        -1.501         0.477        -2.128        -0.935

           TAU

              I6$3          I7$1          I7$2          I7$3          I8$1

              ________      ________      ________      ________      ________

      1         0.755        -1.960        -1.111         0.872        -2.394

           TAU

              I8$2          I8$3

              ________      ________

      1        -1.569         0.524

Mplus final Thresholds:

    I1$1              -1.505

    I1$2              -0.629

    I1$3               0.805

    I2$1              -1.808

    I2$2              -0.783

    I2$3               0.613

    I3$1              -4.426

    I3$2              -1.199

    I3$3               1.984

    I4$1              -0.624

    I4$2               0.669

    I5$1              -1.881

    I5$2               0.598

    I6$1              -2.987

    I6$2              -1.312

    I6$3               1.061

    I7$1              -2.311

    I7$2              -1.310

    I7$3               1.028

    I8$1              -2.906

    I8$2              -1.904

    I8$3               0.637

Lavaan final threshold estimates:

t1i1|t1 -2.394
t1i1|t2 -1.001
t1i1|t3 1.282
t1i2|t1 -2.394
t1i2|t2 -1.036
t1i2|t3 0.812
t1i3|t1 -2.394
t1i3|t2 -0.648
t1i3|t3 1.073
t1i4|t1 -1.111
t1i4|t2 1.192
t2i1|t1 -1.501
t2i1|t2 0.477
t2i2|t1 -2.128
t2i2|t2 -0.935
t2i2|t3 0.755
t2i3|t1 -1.960
t2i3|t2 -1.111
t2i3|t3 0.872
t2i4|t1 -2.394
t2i4|t2 -1.569
t2i4|t3 0.524

I guess I realized part of the problem is that the diagonals on the $theta matrix are being estimated in Mplus, but not in Lavaan.  How do I get lavaan to estimate $theta parameters.  I hope that helps and is not confusing.  Otherwise I can post a model if that makes it easier.

Thanks.

[yrosseel]

On 05/05/2013 07:40 PM, merm.m...@gmail.com wrote:

> I guess I realized part of the problem is that the diagonals on the
> $theta matrix are being estimated in Mplus, but not in Lavaan. How do I
> get lavaan to estimate $theta parameters.

This explains it. lavaan (0.5-12) does not yet support the so-called
'theta' parameterization (where the theta diagonal elements are free
parameters). lavaan only supports the delta parameterization.

But in most cases, the two parameterizations are equivalent (same model
fit).

Yves.

[merm.m...@gmail.com]

Thanks Yves.  But if the theta paramaters are not being estimated would that explain for why Mplus final threshold values are not the same as lavaans?  Although the models are same, the different parametrization will result in different threshold values and thus parameter estimated (such as factor loadings and variances) between Mplus and lavaan for categorical sem models, yes?

All your help is greatly appreciated.

Tav.

[yrosseel]

On 05/06/2013 06:52 AM, merm.m...@gmail.com wrote:
> Thanks Yves. But if the theta paramaters are not being estimated would
> that explain for why Mplus final threshold values are not the same as
> lavaans?

Absolutely. In the theta parameterization, theta is fixed to 1.0, and
this affects the values of other parameters.

See the Mplus webnote about this:

www.statmodel.com/download/webnotes/CatMGLong.pdf

Yves.

[Michael Paul Grosz]

Hi Yves,

I am not completely sure whether I understand the difference between delta and theta parametrization outlined in the Mplus webnote.
The theta parametrization allows one to test for invariance across groups with regard to the residual variances. However, if one wants to test the invariance of thresholds and loadings across groups, both, delta and theta parametrization, are useable.
right?

best,
Michael

[Yves Rosseel]

On 10/27/2014 04:19 PM, Michael Paul Grosz wrote:
> Hi Yves,
>
> I am not completely sure whether I understand the difference between
> delta and theta parametrization outlined in the Mplus webnote.
> The theta parametrization allows one to test for invariance across
> groups with regard to the residual variances. However, if one wants to
> test the invariance of thresholds and loadings across groups, both,
> delta and theta parametrization, are useable.
> right?

Right.

Yves.

[Phil Wood]

Not to revitalize an old thread, but is there a difference in how the two programs handle missing data? For example, ifi I write in Mplus and lavaan, I get the same thresholds if I make a data set with no missing data, but different thresholds if I have missing data.

TITLE:  

DATA:

  FILE IS "mydata.txt";

listwise=on;

ANALYSIS:

  TYPE IS MISSING;

  ESTIMATOR IS wlsmv;

  parameterization=delta;

(follows a tau equivalent factor model)

I get different answers from lavaan with call:

model<-"

! regressions 

   f=~L1*qpls5mw0

   f=~L1*qpls5mw1

   f=~L1*qpls5mw2

   f=~L1*qpls5mw3

   f=~L1*qpls5mw4

   f=~L1*qpls5mw5

   f=~L1*qpls5mw6

   f=~L1*qpls5mw7

   f=~L1*qpls5mw8

   f ~~ 1*f

qpls5mw0 | th0*t1

qpls5mw1 | th1*t1

qpls5mw2 | th2*t1

qpls5mw3 | th3*t1

qpls5mw4 | th4*t1

qpls5mw5 | th5*t1

qpls5mw6 | th6*t1

qpls5mw7 | th7*t1

qpls5mw8 | th8*t1

";

result<-lavaan(model, data=pls5data,parameterization="delta", 

               missing = "listwise",

               ordered=c("qpls5mw0",

                 "qpls5mw1",

                 "qpls5mw2",

                 "qpls5mw3",

                 "qpls5mw4",

                 "qpls5mw5",

                 "qpls5mw6",

                 "qpls5mw7",

                 "qpls5mw8"),estimator="WLSMV");

any thoughts? TIA Phil

[Terrence Jorgensen]

I think Mplus uses pairwise deletion by default when fitting actual models (e.g., TYPE = GENERAL), which you can do in lavaan by setting missing = "pairwise".  However, in Mplus you set:

listwise=on;

ANALYSIS:

  TYPE IS MISSING;

Does TYPE IS MISSING return summary statistics and proportions of missing data per variable?  I don't see that TYPE option listed in their manual:

https://www.statmodel.com/HTML_UG/chapter16V8.htm

Perhaps it only deleted missing cases per variable, rather than cases that have missing values on any variable in USEVARIABLES (which you did not specify).  Difficult to tell without attaching the Mplus output file.

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

[Patrick (Malone Quantitative)]

In Mplus, TYPE IS MISSING is obsolete, having become the default a
number of years ago, instead of the old default of listwise. LISTWISE
IS ON was added as an option instead. I'm not sure what happens with
both of them specified, as they are intended to do opposite things, so
I'm not sure what you are expecting from that.

On Sat, Nov 14, 2020 at 6:01 PM Phil Wood <philli...@gmail.com> wrote:
>
> I already tried that and, for good measure, have that option turned on in lavaan. They are still different, but thanks, I should have made that clearer:
> For documentation purposes, here's the essential code of each:

> DATA:
> FILE IS mydata.txt";
> listwise=on;

> VARIABLE:
> NAMES ARE all-the-names;
> USEVARIABLES ARE just-the-items;
> MISSING IS .;
> categorical is
> just-the-items;

> ANALYSIS:
> TYPE IS MISSING;
> ESTIMATOR IS wlsmv;
> parameterization=delta;

> (tau-equivalent model follows)
> and for lavaan:
> model<-"

> "qpls5mw8"),estimator="WLSMV",optim.method="BFGS",optim.dx.tol = .0001);
> summary(result, fit.measures=TRUE,rsquare=TRUE, standardized=TRUE);
> Thanks, folks, hope this clears the question up a bit.

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Patrick S. Malone, Ph.D., Malone Quantitative
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