Random intercepts PreviousNext
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Message/Author
 Bill Roberts posted on Thursday, May 09, 2002 - 8:01 am
Are random intercepts at the between level the default for Mplus two-level models? If so, are the intercepts random by default for observed and latent variables?
 Bengt O. Muthen posted on Friday, May 10, 2002 - 7:16 am
The answer to both of your questions is yes.
 bobh posted on Friday, June 11, 2004 - 2:06 pm
How do I specify a two-level random intercepts (fixed slopes) model in Mplus?
 Linda K. Muthen posted on Saturday, June 12, 2004 - 7:34 am
I have adapted the ANALYSIS and MODEL commands of Example 9.1 from the Mplus User's Guide to have a fixed slope.

ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
y ON x;
%BETWEEN%
y ON w;
 Bobh posted on Sunday, June 13, 2004 - 8:58 am
I don't have a between-level covariate, W. Will this work?

ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
y ON x;
%BETWEEN%
y;
 bmuthen posted on Sunday, June 13, 2004 - 9:48 am
Yes. And, you don't have to mention y in the between part - its mean and variance will be estimated as the default.
 Guo Boliang posted on Friday, June 18, 2004 - 12:21 am
groupcentering (x);
ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
y ON x;
%BETWEEN%
y;

can this command work?
 bmuthen posted on Friday, June 18, 2004 - 8:45 am
Yes. Except that your centering statement does not use the right grammar, it should be

centering = groupmean(x);

And, grandmean centering is perhaps more common.
 Guo Boliang posted on Friday, June 18, 2004 - 11:29 pm
Dr.Muthen,
following is my command, i wanna center the X variable in each group like the HLM "ADD vatiable cetering on group" doing, but MPLus SAY it can not work, what is the problem?
thanks,
boliang

BETWEEN = od;
centering = groupmean (bad10);
CLUSTER IS class;
ANALYSIS:
TYPE = TWOLEVEL RANDOM Missing H1;
ALGORITHM = INTEGRATION;
INTEGRATION = 10;

MODEL:
%WITHIN%
s|newac ON bad10;
bad10 ON newac@0;


%BETWEEN%
bad10 newac ON od;
output:
sampstat TECH1 TECH8;

*** ERROR in Variable command
GROUPMEAN centering can be applied to WITHIN variables only.
Unable to center variable: BAD10
 Linda K. Muthen posted on Saturday, June 19, 2004 - 11:05 am
You need to add WITHIN = BAD10; to the VARIABLE command.
 Guo Boliang posted on Sunday, June 20, 2004 - 8:17 pm
even I add the withn = bad10, the command can not work too. following is the command and the error message.
thanks for your attention and help.


USEVARIABLES ARE bad10 newac od class;
MISSING IS *;
WITHIN = BAD10;
BETWEEN = od;
centering = groupmean (bad10);
CLUSTER IS class;

ANALYSIS:
TYPE = TWOLEVEL RANDOM Missing H1;
ALGORITHM = INTEGRATION;
INTEGRATION = 10;

MODEL:
%WITHIN%
s|newac ON bad10;
bad10 ON newac@0;
%BETWEEN%
bad10 newac ON od;
output:
sampstat TECH1 TECH8;

*** ERROR in Model command
Within-level variables cannot be used on the between level.
Within-level variable used: BAD10
 bmuthen posted on Sunday, June 20, 2004 - 9:14 pm
You have bad10 as an x variable on Within and as a y variable on Between - is that your intention? If you want bad10 to have Between variation you cannot use the centering command. In such a situation you need to center the variable yourself - you can use the Define command.
 Anonymous posted on Monday, January 10, 2005 - 8:51 am
I want to run a two-level model with a random intercept and a random slope but no level 2 covariates. The code I used is

ANALYSIS: Type = Twolevel Random;
Algorithm = Integration;

MODEL:
%WITHIN%
a | y on x;
y*1;

%BETWEEN%
[a*.6];
a*.160;

The problem is that I get the error message:

*** WARNING in Model command
Variable on the left-hand side of an ON statement in a | statement is a
WITHIN variable. The intercept for this variable is not random.
Variable: Y

I want this intercept to be random, but can't seem to find a statement to make it random. What should I put in my program file to do this? From your reply to an ealier post, I thought this would be put in by default, but clearly that's not happening here.

Sorry if this is a bone-headed question.
 Linda K. Muthen posted on Monday, January 10, 2005 - 8:13 pm
It sounds like you are putting y on the WITHIN list. You should not do this.
 Anonymous posted on Monday, January 24, 2005 - 2:40 pm
Dr. Muthen,
I am trying to use longitudinal growth curve model to analyze our data which is clustered. However, we don't have a between-level covariate. So here's the modelI am trying to fit:

y_{ijt} = a_{ij}+ b_{ij}t_{ij} + e_{ijt},

a_{ij} = a1_{j} + b1*x_{ij} + e1_{ij},

b_{ij} = a2_{j} + b2* x_{ij} + e2_{ij},

a1_j = a3 + e3_j,

a2_j = a4 + e4_j,

where subscripts i is for individual, j is for school and t is for time. Outcome variable is denoted as y_{ijt}, subject level covariates is x_{ij}. By reading the User's Guide, I wrote down the following code:

VARIABLE:
NAMES ARE school x1 x2 x3 x4 y1 y2 y3 y4 y5;

USEV = x1 x2 x3 x4 y1 y2 y3 y4 y5 school;
CLUSTER = school;

ANALYSIS:
TYPE = TWOLEVEL RANDOM;

MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@4 y5@8;
iw ON x1 x2 x3 x4;
sw ON x1 x2 x3 x4;
%BETWEEN%
???

However, it is not clear for me how to specify the school effect in the %BETWEEN% part of the model. Could you provide any guide on this? thanks a lot for your help.
 bmuthen posted on Monday, January 24, 2005 - 6:04 pm
The Between part of the model should be

ib sb | y1@.... (as on Within)

- here ib and sb are your a1_j and a2_j effects. If you write out your first equation including the terms of a1_j and a2_j you see that this makes sense (they form a growth model on between). Try it out and check that you get the parameters you expect (and only those).
 Anonymous posted on Tuesday, January 25, 2005 - 12:42 pm
Dr. Muthen,

Thanks so much for your answer. However, I tried the following code:

MODEL:
%WITHIN%
iw sw | y1@0 y2@1 y3@2 y4@4 y5@8;
iw sw ON x1 x2 x3 x4;
%BETWEEN%
ib sb | y1@0 y2@1 y3@2 y4@4 y5@8;

and get the following error messages for each of the x's:
*** WARNING in Model command
Variable is uncorrelated with all other variables on the BETWEEN level:
X1
*** ERROR in Model command
Variable is a y-variable on the BETWEEN level but is an x-variable
on the WITHIN level: X1

All the x's are dichotomous. Can you point out why I get these error messages? Thank you very much for your help.
 Linda K. Muthen posted on Tuesday, January 25, 2005 - 2:09 pm
You don't have any x's on the between level so you should declare them as within only by putting them on the WITHIN list in the VARIABLE command. This is just a warning to let you know this.
 Anonymous posted on Wednesday, January 26, 2005 - 9:04 am
Dr. Muthen,
Thanks for pointing this out. It works.
 Pancho Aguirre posted on Wednesday, November 02, 2005 - 2:08 pm
Hello Bengt and Linda,

Searching the Mplus dicussion board I found a posting with its reply from 4 years ago. (i have attached it below).
My question is in regards to Bengt's answer "In Version 3 of Mplus, random slopes for observed covariates will be included.", Does version 3 handles random slopes for latent covariates?



"Hello -- I am learning Mplus so that I can estimate some multilevel path models, but I'm afraid I've gotten confused.

In a standard mixed regression model, you can estimate a level-1 regression where x_1 and x_2 predict y, and it is possible to get random components for the intercept and both regression parameters over level-2 units. However, as best as I can tell, in Mplus it is only possible to get a random intercept but NOT random slopes in the same situation.

Is there a straightforward way to understand why this is so? Is the answer to this the same reason why in a multilevel CFA in Mplus you can only get random intercepts in the indicators but the factor loading matrices are forced to be invariant across level-2 units?

Thank you very much.



Bengt O. Muthen posted on Wednesday, November 14, 2001 - 6:52 am

You are correct that random slopes are not part of the Mplus multilevel model for cross-sectional data. Latent variable modeling has traditionally considered mean and covariance structure models. With random slopes, there is no one covariance structure, but the covariance structure changes for each covariate value. See, for example, the Raudenbush chapter in the Collins, Sayer book. In Version 3 of Mplus, random slopes for observed covariates will be included."
 Linda K. Muthen posted on Wednesday, November 02, 2005 - 6:43 pm
Yes.
 Oliver posted on Monday, February 13, 2006 - 5:59 am
I have a question regarding the interpretation of regression coefficients in random-intercept models in Mplus. I am interested in a simple two-level model with one independent variable on level 1 X_ij and the corresponding aggregrated scores on level 2 X_.j. In HLM notation the model could be written as:

Y_ij = b_0j + b_1j * X_ij + e_ij

b_0j = g_00 + g_01 * X_.j + u_0j

b_1j = g_10

The obvious way to specify this model in Mplus would be

1) Mplus model

%within%
Y on X;

%between%
Y on X;

Now I am not sure how to interpret the regression coefficient on level-2. Is the level-1 predictor variable group-mean centered or grand-mean centered?

So I specified two additional models using the centering option in Mplus.

2) grand-mean centered

within = X;
between = X_average;
centering = grandmean(X);

%within%
Y on X;

%between%
Y on X_average;

3) group-mean centered

within = X;
between = X_average;
centering = groupmean(X);

%within%
Y on X;

%between%
Y on X_average;


I compared the level-2 regression coefficient of model 1 (“Mplus”-model) to the ones I obtained when I use the centering options – and which I could replicate in an HLM analysis. Interestingly, the value of the level-2 regression coefficient for the “Mplus” model was not near to the coefficient of the grand-mean or of the group-mean centered model.

a) How would you interpret the level-2 coefficient in model 1?
b) Could you explain to me how the level-2 regression coefficient in model 1 is related to the level-2 coefficients in model 2 and model 3?
c) Given that the interpretation of the level-2 coefficient in model 2 and model 3 is well established in the multilevel literature, could you imagine a data constellation in which you would recommend using the coefficient of model 1?

Thank you very much for your help!
 bmuthen posted on Tuesday, February 14, 2006 - 4:59 pm
Model 1 in Mplus takes x to be a variable with both within and between-level variation, decomposing the variable into two orthogonal components, thereby using an estimated between-level component of x as the between-level predictor. This between-level predictor has a mean, so is not centered. This between-level variable is approximately the same as a variable created from the cluster-means for x (perhaps that is your approach/model 2, except you subtract the overall mean?). The difference is that with unbalanced data (different cluster sizes) the Model 1 approach may be more robust to outliers in that a small cluster with an outlier mean will be downweighted using a normality assumption. I think the Raudenbush & Bryk book talks about related issues in terms of "precision-weighted means".

I'd be interested in seeing your application if you get large differences between 1 and 2.
 Oliver posted on Friday, February 17, 2006 - 2:17 am
Dear Dr. Muthen,

I created a balanced data set by randomly selecting 10 students out of each class. My data set contains 76 classes. The dependent variable is a standardized mathematics achievement test (ICC = .52) and the independent variable is the student perception of disruptions during the lesson (ICC = .26). I also aggregated the student perceptions for every class across students and included the class means into the model on level-2 (only for Model 2 and 3). This model is essentially the contextual analysis model discussed by Raudenbush and Bryk in chapter 5 of their book.
I obtained the following results for the three models (unstandardized coefficients, standard errors in brackets):

Model 1 (Mplus)

Analysis: Type is twolevel;
Model:
%within%
math on disruption;
%between%
math on disruption;

g10 = -.095 (.060)
g01 = -.863 (.338)

Model 2 (grand-mean centered, a_disruption is the aggregated class mean)

within = disruption;
between = a_disruption;
centering = grandmean(disruption);
Analysis: Type is twolevel;
Model:
%within%
math on disruption;
%between%
math on a_disruption;

g10 = -.094 (.044)
g01 = -.608 (.263)

Model 3 (group-mean centered)

within = disruption;
between = a_disruption;
centering = groupmean(disruption);
Analysis: Type is twolevel;
Model:
%within%
math on disruption;
%between%
math on a_disruption;

g10 = -.095 (.065)
g01 = -.701 (.263)

Model 2 and Model 3 show the expected relationship between the coefficients (Raudenbush & Bryk, 2002, p. 139). The contextual effect g01 in Model 2 is (almost) equal to the result of subtracting the coefficients in Model 3: -.608 = -.701 – (-.095). But it is difficult for me to interpret the level-2 regression coefficient (g01) in Model 1. You said that Model 1 decomposes the independent variable into two orthogonal components; but isn’t that the idea of group-mean centering (Model 3)?

Thank you very much for your help!
 bmuthen posted on Friday, February 17, 2006 - 5:09 pm
Since this topic is of general interest, we decided to give you a fuller answer by writing up a little note on this. It will be available shortly.
 bmuthen posted on Friday, February 24, 2006 - 6:44 pm
Tihomir Asparouhov has taken the lead on writing a note on this topic. If you send us your email address to support@statmodel.com, we will send the pdf to you. Later on, it will be posted together with Mplus Monte Carlo simulation runs.

The message of the note is that Model 1 (in your notation above) is the best way to approach this analysis. The other approaches can give biases in the between-level slope and therefore also in the "compositional effect". The bias increases when the cluster size decreases and when the ratio of within to between variance for x increases. This is perhaps a little known fact so the note should help. In many applications, however, the bias is expected to be small.

Could you make your data available to us?
 kanako ishida posted on Wednesday, December 06, 2006 - 11:07 pm
I think I have a very basic question. I want to do two-level logistic regression analyses and after running the model, I want to get a predicted probability based on the model, but holding several variables at a particular constant (like their respective means) while allowing variation for other independent variables of interest. For example, I want to see the probability of dropping out of high school and how it varies by race/ethnicity and years of education of their mother, while holding constant gender and socioeconomic status at their means (or mode). Can Mplus do it? If it does, how?
Thank you!
 Linda K. Muthen posted on Thursday, December 07, 2006 - 9:04 am
No, Mplus does not do this.
 Fernando Terrés de Ercilla posted on Sunday, June 10, 2007 - 11:31 am
After running a multigroup multilevel regression with random slopes I get two influence (outliers) measures OUTINFL and OUTINFLC. ¿Whats the meaning of each of this measures (I hoped only one)? Many Thanks.
 Linda K. Muthen posted on Monday, June 11, 2007 - 10:00 am
OUTINFL is for the within-level outliers and outinflc is for between-level outliers.
 Jeremy Flaherty posted on Wednesday, May 28, 2008 - 8:38 pm
Regarding a post above from 17 Feb 2006:

Is it okay when the contextual effect is not exactly equal to the difference of the between and within coefficients?

It seems that most examples I see, such as in Bryk and Raudenbush (1992:122) and Snijders and Bosker (1999:87), they are always exactly equal. When I use Mplus they are often off by a couple of thousandths (sometimes as much as a hundredth).
 Linda K. Muthen posted on Thursday, May 29, 2008 - 3:08 pm
They are exactly equal because that is how the contextual effect is defined and computed - you may be misinterpreting the results. Please send your output and license number to support@statmodel.com if you want help on this.
 Paola posted on Friday, January 22, 2010 - 7:44 am
Dear Linda,
I am running a random intercept model on a longitudinal data set in long format, this is the code

BETWEEN= chd sex sexchd;
WITHIN = alcoh depres age agesq;
CLUSTER = id;
Define: sexchd=chd*sex;
ANALYSIS: TYPE = TWOLEVEL;
estimator=ml;

MODEL:
%WITHIN%
qol ON age agesq alcoh depres;

alcoh depres;
/to use all available data/

%BETWEEN%
qol ON chd sex sexchd;

I would like to know what kind of covariance matrix structure mplus uses when I have the data in long format for the random intercept model (I assume is independent, but I am not sure), and what the difference would be in the covariance matrix structure if I set the data to be in wide format.
Also how can I obtain the covariance matrix? is it output:tech4 correct?
 Linda K. Muthen posted on Friday, January 22, 2010 - 9:35 am
The setup looks correct. With long format residual variances of the outcome and regression coefficients of the time-varying covariates are equal across time. With wide format, they are not.
 Paola posted on Friday, January 22, 2010 - 11:39 am
Thank you Linda,
is there a way to set up the variances non to be equal across time when analysing this data in long format?
 Linda K. Muthen posted on Friday, January 22, 2010 - 12:30 pm
No.
 Mathias Höglund posted on Tuesday, May 11, 2010 - 11:05 am
Hello,

I know this topic was discussed some years ago but I'm trying to sort this out for myself. If I model an observed variable X on both the within and the between level the between level variable is a random intercept.

Could you elaborate on what the intercept refers to and how it is formed by mplus? I'm trying to figure out how the mplus approach differs from using cluster means at the between level and centering the within variable?

As always, I appreciate your kind help!
 Bengt O. Muthen posted on Tuesday, May 11, 2010 - 11:35 am
It's really a random mean in your setting. See slide 16 - in the Topic 7 handout on our web site, where y takes the role of your x and eta takes the role of the latent between-level part. Note that this is simply 1-way random effects ANOVA.

Also, you want to read:

Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203-229.

which is on our web site. And you want to look at UG ex9.1. which describes this.
 Mathias Höglund posted on Wednesday, May 12, 2010 - 8:20 am
Thank you Bengt! That does help a lot. It really is a good paper that makes this perfectly clear.
 Mathias Höglund posted on Wednesday, May 19, 2010 - 2:15 pm
Thanks again for your help. I have a short follow up question that I'm trying to figure out:

1 - When I model a variable X on two levels as in example 9.1. without specifying the centering, how does mplus treat the within variable? Is it simply using the actual observed values or is it decomposing or centering this variable?
2 - What would in this case be the advantage of centering a variable?
 Linda K. Muthen posted on Wednesday, May 19, 2010 - 2:52 pm
1. Example 9.1 shows two approaches to handling x. In both approaches the variable is not modified in any way.

2. Centering is usually done to aid in interpretation, for example, in a regression the intercept of a centered variable becomes a mean.
 Mathias Höglund posted on Thursday, May 20, 2010 - 12:57 am
Thanks a lot Linda,

Actually I have to correct myself. I am actually not mentioning my variable X on the within statement. Am I correct that:
a) this means that the variable is then decomposed into two uncorrelated latent variables?
b) this essentially involves a latent group-mean centering of the within level X?
c) this is the MLC model discussed in
Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008)?
 Linda K. Muthen posted on Thursday, May 20, 2010 - 11:32 am
Yes, yes, and yes.
 Tor Neilands posted on Thursday, September 09, 2010 - 10:19 am
I am fitting a multiple groups multilevel regression model to longitudinal data with five groups. There is a single continuous outcome explained where time is represented by three linear spline variables whose values can vary within observations (within level). Remaining explanatory variables are measured at the subject (between) level.

The goal of the analysis is to generate expected values of the outcome for each spline knot for each of the five groups and then to compare those expected values by defining new parameters representing their differences using MODEL CONSTRAINT, at the mean values of the other covariates. I read in the Mplus 6 documentation that Mplus can grand-mean center variables, which is a great feature. I noticed that in multiple groups analysis the grand-mean centering feature of Mplus will center observations around the group's mean rather than the overall mean for the whole sample. I was curious to know what the thinking was behind setting up the grand-mean centering feature of Mplus in this way? I would think for my type of application I would want to grand-mean center using the whole sample mean so as not to introduce bias in the group comparisons of the outcome, but wanted to make sure I wasn't missing a reason to use the within-groups means instead for grand-mean centering?

Thanks for any insights you can share.

Tor Neilands
 Linda K. Muthen posted on Thursday, September 09, 2010 - 3:21 pm
Each group represents a different population so in line with standardizing using each group's standard deviations, centering is done using each groups means. You can use the DEFINE command to center using the overall mean if you want to.
 Daniel E Bontempo posted on Wednesday, September 22, 2010 - 8:51 am
I wanted to use example 9.1, as modified in the posting above, for a random intercept-only model, as the basis for a monte carlo study to look at power.

I have a continuous outcome repeatedly measured 40 times on 80 people. I have two binary covariates. One which groups people into two groups of 40, and the other that designates stimulus form A or B, each repeated 20 times within person.

I have:
-------------
Montecarlo:
names are TE NP ageGrp;
nobservations = 3200;

cutpoints NP(1) ageGrp(1);

ncsizes = 1;
csizes = 80 (40);

seed = 58459;
nreps = 500;

between = ageGrp;
within = NP;


ANALYSIS: TYPE = TWOLEVEL RANDOM;

model population:

%within%
NP*1;

TE on NP*1;
TE*1;

%between%
ageGrp*1;

TE on ageGrp*1;
[TE*2];
TE*.5;

----------

But I have a few questions/issues.

I would like to get the repeated NP factor on both levels, but CUTPOINTS seems to work only for variables on a single level.

I would also like to get the cross-level interaction term for the two predictors, but am not sure how to get such values generated.
 Linda K. Muthen posted on Wednesday, September 22, 2010 - 11:21 am
If you want NP on both levels, do not put it on the WITHIN statement.

Cross-level interactions are obtained using a random slope model. See Example 9.2 and mcex9.2.inp for the Monte Carlo counterpart of Example 9.2.
 Daniel E Bontempo posted on Wednesday, September 22, 2010 - 11:45 am
But, as I say, the cutpoint will not work then.

*** ERROR in MONTECARLO command
Cutpoints are currently only supported for BETWEEN or WITHIN variables.
Cutpoints for variable NP were specified.

---------


While the interaction is cross-level as I specified it, I ideally want NP on both levels, so the WP interaction would be manifest. I guess the NP*ageGrp interaction would be a latent BP-level NP with manifest BP-level ageGrp.

Does this require XWITH? It seemed that XWITH only worked with random slope, and was not accepted syntax for random intercept-only. Is this correct?

Perhaps there is a better way to simulate a random intercept only model with two binary factors, one of which on the BP level.
 Linda K. Muthen posted on Wednesday, September 22, 2010 - 12:30 pm
See Slide 39 of the Topic 7 course handout to see how the random slope model results in a cross-level interaction. You do not use XWITH. NP does not need to be on both the within and between parts of the MODEL command.
 Vlad posted on Wednesday, February 02, 2011 - 12:16 pm
Hello,
I have question regarding to mplus output. Here is the partial code of mplus.
cluster=country;
nominal=y;
within=x;
between=;
analysis: type=twolevel;

model:
%within%
y on z x;
z on x;
%between%

savedata:
file is J:\mplusm\work.txt;
save is fscores;
format is free;

Since y is nominal with 4 categories and z is continuous,thus, I have 4 continuous intercepts(3 of them belong to y and 1 to z). When I open the saved output, intercepts of y do not vary across clusters (country). Why do these intercepts constant across countries?
Regards,
V
 Bengt O. Muthen posted on Wednesday, February 02, 2011 - 5:00 pm
Make sure that you estimate variances for the 4 intercepts on the Between level.
 Bernhard Swoboda posted on Thursday, October 06, 2011 - 1:32 am
My question refers to a path on level2 (random intercept) which I explored within a median split (2 groups - like multi group).

My model: I do have a two-level model with a random intercept and slope. Level1 = consumers; Level2 = Brands.
The random intercept path was not significant with a high standard error. Then I splitted the sample according a variable "consumer identity" which is a variable actually on level1. The random intercept path becomes significant and is theoretically sound. Implementing this, I run the model with two different samples.
My questions are:
(1)Can I use a level1 variable (distinct for each consumer on level 1) to split the sample for a path on level2?
(2)Does this refer to a third level but only having two groups on the third level via median split?

Thanks for your help.
 Linda K. Muthen posted on Thursday, October 06, 2011 - 8:35 am
1. You need to use a level 2 variable to split the sample if you want to maintain independence of observations. Using a level 1 variable will violate that.

2. No.
 Christine Victorino posted on Monday, October 17, 2011 - 8:37 am
Hello,

I have 2 questions:

1. I'm conducting a two-level SEM with one factor (w/4 indicators) regressed onto a second factor (w/7 indicators) at the within level. I am estimating random intercepts for all 11 indicators using a single factor at the between level. I have included one covariate at the between level. 10/11 of the random intercepts are positive and significant, however 1/11 of the random intercepts is negative and significant. Can I interpret these intercepts as occurring due to the between-level covariate? For example, Hox (1995) wrote "if B01 is positive and significant, we conclude that school career outcome in large schools is higher than in small schools"

B0j = B00 + B01*Zj + u0j,
where B01 is the slope of the random intercept and Zj is school size (covariate).

2. If I do not include a covariate at the between level, can I interpret these as simply group level effects (as in one-way ANOVA)?

Thanks so much!
 Bengt O. Muthen posted on Monday, October 17, 2011 - 9:43 pm
1. I assume that when you talk about random intercepts being positive or negative, you are really talking about the between-level residual variances for the random intercept indicators of the between-level factor. You should check if you get a negative random intercept variance without the between-level covariate. Note also that these variances are typically small due to higher between-level correlations (higher reliability).

2. The between-level intercepts are cluster-level effects. You are doing something in the spirit of random effects ANOVA, but with a factor structure.
 Christine Victorino posted on Tuesday, October 18, 2011 - 5:58 am
Dr. Muthen,

I also read your 1994 paper (Multilevel Covariance Structure Analysis). For clarity, the random intercepts are the residual variances at the between level?

Between Matrix = (Lambda)*(PsiB)*(Lambda') + ThetaB,

where Lambda is the vector of factor loadings, PsiB describes the magnitude of the non-independence, and ThetaB represents the group-level residual variance.

How then do I interpret the factor loadings (Lambda) for the indicators at the between level?

If you know of any applied papers that conduct ML-SEM with random intercepts, please let me know.

With gratitude,
Christine
 Bengt O. Muthen posted on Tuesday, October 18, 2011 - 9:28 am
No, the random intercepts are the variables that you apply your Between Matrix expression to - they are the factor indicators on Between. Doesn't matter that they are latent variables.

Factor loadings are interpreted in line with regular factor analysis, but applied to the random intercepts - i.e. the between-level variation of your variables.

We discuss between-level FA in our Topic 7 video and handout. There are papers listed under Multilevel SEM in our Paper's section on the web site.
 nick depp posted on Wednesday, November 09, 2011 - 11:33 pm
In the XY-coordinate plane, line L and line K intersect at the point (4,3). Is the product of their slopes negative?

1) The product of the x intercepts of line L and K is positive.

2) The product of the y-intercepts of line L and k is negative.
 Linda K. Muthen posted on Thursday, November 10, 2011 - 11:56 am
What is your Mplus MODEL command?
 Stefan Luebeck posted on Monday, January 16, 2012 - 7:38 am
Hello, i do have a few questions beeing a beginner with mplus.

In my multi-level model for my master theses, i'd like to calculate unstandardized coefficients in form of a random-intercept-model with fixed effects of the level-1 variables (the individuals). The parameters should be estimated with the restricted-maximum-likelihood-method. In addition the asymptotic standard-errors are to be used. I already used the grand-mean centering option for all independent variables. Also the explained variances for each level shell always be calculated in relation to the nullmodel.

Because I haven't used mplus before, i wonder how the input should look like for the level-1 and level-2 model.

I already tried to find information about it, but didn't really find much.

I hope i also posted this in the correct section.
 Stefan Luebeck posted on Monday, January 16, 2012 - 9:39 am
Hello again,
here some additional information: The dependent variable (perception of public bads, ordinal scaled) as well as the independent variables on level-1 are from a survey about selfreported delinquency done in several schools in a german city. The level-2 variables are partly metric as well as some factorscores are used, for ex. a factorscore for problematic social structure, which combines average income, percentage of foreigners and percentage of single-parent households. The level-2 data used are official data from the statistics bureau of the town where the survey was done.
 Linda K. Muthen posted on Monday, January 16, 2012 - 1:38 pm
Mplus uses full-information maximum likelihood. REML is not available.

See Examples 9.1 and 9.2 in the user's guide and the Topic 7 course handout on the website.
 Sara Guediri posted on Wednesday, August 07, 2013 - 9:37 am
Hello,

I'm trying to fit a random intercept model with all variables modelled at the within and between level.

usevariable = Lsati TB TC Risko TBxR;
cluster = team;

analysis:
type = twolevel;

model:
%within%
Lsati on TB TC Risko TBxR;

%between%
Lsati on TB TC Risko TBxR;


In the output the between-level coefficients and R-square tend to be large (some standardised coefficients are > 2.0 and R-square as large as .98), but all non-significant. Is this statistically sound? Can you recommend a citation to read up on this particular issue?

Thank you
 Linda K. Muthen posted on Wednesday, August 07, 2013 - 12:03 pm
Please send the output and your license number to support@statmodel.com.
 Paola posted on Wednesday, January 22, 2014 - 8:22 am
Hello, I would like to know if in version 7.11 is possible to use auxiliary variables (that I know are predictive of missing data and are not part of the model) with random intercept models
TYPE=TWOLEVEL
Thank you
 Linda K. Muthen posted on Wednesday, January 22, 2014 - 10:11 am
If you mean the AUXILIARY missing option, no. If not, which AUXILIARY option do you refer to.
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