3-level analysis by HLM and Mplus PreviousNext
Mplus Discussion > Multilevel Data/Complex Sample >
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 bmuthen posted on Tuesday, March 26, 2002 - 10:39 am
A frequent question is how 3-level modeling of growth of students within schools compares to HLM-type analysis. Here are some answers.

Actually, these analyses are one and the same. The 3-level HLM formulation describes across-time variation at level 1 involving random intercept and slope coefficients, level 2 studies the across-student variation of those coefficients, while level 3 studies their across-school variation. In the latent variable context, level 1 and level 2 are combined into the "Within" part of the model, i.e. the part describing variation across students. The "Between" part describes across-school variation and corresponds to level 3 of HLM. In this way, the 3-level HLM model is turned into a 2-level latent variable model. The fact that level 1 and level 2 are both considered in the Within part of the latent variable model is due to viewing the level 1 across-time variation as a multivariate observation vector rather than as a univariate repeated observation. Level 1 of the Within part is the latent variable measurement model part and level 2 of the Within part is the structural part.

So in summary, Mplus estimates a random coefficient model and the Between component intercept and growth coefficients are representing variation across clusters in the coefficients defined for Within (students), just as in HLM analysis. If you use the ML estimator you get the same estimates.
 aboabdulmalik posted on Thursday, September 29, 2005 - 10:05 pm
Hi,
I am examining the mediational effect of (COLL) on the relationship between CL and TS. I have the predictor CL at the school level, the mediator COLL at the school level, and the outcome variable, TS, at the individual level. Thus, it is 2 > 2 > 1 (i.e., CL > COLL > TS; with a direct path from the predictor to the outcome as well).

I am only familiar with the software HLM, through my independent reading. I wanted to examine the mediational effect but i was not able to regress the mediational variable on the predictor variable. Regressing the mediator on the predictor is one essential equation to examine mediational models. Can i examine this equation using OLS through SPSS regression. The rationale is that both the mediator and the predictor variables are both at the school level. While for other equations, i am using HLM to regress the outcome on the predictor and the outcome on the mediator.
If i use SPSS regression to regress the mediator on the predictor, how comparable the coefficients produced by SPSS and HLM. Is there any implimintation required while running the regression. Or, is there any function within the software HLM to run a mediational modeling. I know that MPlus enables to examine the mediational modeling, but my limited time and limited statistics will not help me. The best i can use is the simple 2-level HLM.
I appreciate your help.

Another question is related to examining the assumptions before using HLM. I checked my data in terms of outliers, normality, and linearity through SPSS. I followed Tabachnick and Fidell's 2001) discussion of regression assumptions. My question, then, is there any examinations that are specific to HLM and how to run these examination. Can you refer me to any published work with this regard.
Thank you
 bmuthen posted on Friday, September 30, 2005 - 9:15 am
I think the easiest way to get the correct estimates and particularly the correct standard errors is to use Mplus for this modeling. That would make teh analysis very straightforward.
 Marc Reis posted on Monday, November 21, 2005 - 12:36 pm
Hello,

I would like to use Mplus to estimate the effect of the group-level variable organizational climate on an individual-level outcome. Organizational climate is measured with multiple individual-level (continous) indicators, so there are two scources of error variance for the aggregated organizational climate score for each organizational unit: the variation among the items (due to the fact that they are not perfectly reliable) and among the members of each organizational unit (assuming that there is a "true score" for each group). Since three-level-modeling is not yet available, are there any other ways to estimate the model?

Many thanks for any suggestions!
 Linda K. Muthen posted on Monday, November 21, 2005 - 6:39 pm
Multiple indicators do not count as a level in Mplus because it takes a multivariate approach to multilevel modeling. In Mplus this would be a two-level model if I am understanding you correctly.
 Marc Reis posted on Tuesday, November 22, 2005 - 2:46 am
My problem is that organizational climate is defined as a latent group-level-variable that influences a latent individual-level variable. The idea was to specify the following model:

%within%
DV_within BY i1-i6;

%between%
ORG_CLIMATE BY i7-i12;
DV_between BY i1-i6;
DV_between ON ORG_CLIMATE;

I'am unsure about how Mplus treats i7-i12 in this case? Would ORG_CLIMATE be a "correct measure" of the latent group-level variable? (e.g. would it be reasonable to save a factor score for each group?)
 Linda K. Muthen posted on Tuesday, November 22, 2005 - 7:30 am
You would specify the model as you have done above. You would also have BETWEEN = i7-i12; in the VARIABLE command.
 Marc Reis  posted on Tuesday, November 22, 2005 - 1:15 pm
I tried to specify BETWEEN = i7-i12; in the VARIABLE command, but Mplus doesnīt allow group-level variables to have within-group variation. Note that i7-i12 are individual level indicators that I would like to aggegrate to the group level. So maybe there's another way or I made a mistake.
 bmuthen posted on Tuesday, November 22, 2005 - 4:36 pm
If i7-i12 are scores on individuals, then you don't put those variables on the Between = list. And, you might want to use a within-level factor, say

%Within%

wORG by i7-i12;

%Between%

bORG by i7-i12;

This assumes that you are interested in the within structure of these variables as well as the between structure (and it may not be the same).

Another alternative is to simply aggregate each variable to the between level, i.e. creating cluster means, and then treat these as Between = variables with only between-level variation - and then specify the between-level factor model you have.
 Anonymous posted on Wednesday, November 23, 2005 - 1:39 am
Hello,

I have an idea about the above discussion, maybe this helps. In general there might be two reasons to specify a model with latent variables: The indicators are no perfect measures (--> error variance) and they usually do not measure the factor to the same extent (--> different factor loadings). So requesting factor scores means actually weighting the indicators, doesnīt it?

The question is whether it is necessary to weight the members of a group to obtain a better estimate of the group-level variable. Assuming that there is no special sampling procedure, I donīt see a rationale to weight one group member more than others. So from this point of view, it would be reasonable to simply compute the cluster mean as Bengt suggested, maybe based on the individual-level factor scores. But I am unsure whether to compute the factor scores based on the original covariance matrix or the dissaggregated within covariance matrix.

Maybe someone would like to comment...
 bmuthen posted on Wednesday, November 23, 2005 - 6:37 pm
Comments are invited regarding this. Concerning whether to compute factor scores based on the original cov matrix or within cov matrix, I would say that if factor scores are needed for a multilevel setting, you are better off getting factor scores from a multilevel factor analysis model.
 chantanee posted on Thursday, August 10, 2006 - 2:19 am
The purpose of my study was to find out the relationships among multilevel variables, student variables, classroom variables, and school variables, effected on student science learning achievement of Thai upper secondary school students. The study consisted of 3 sub objectives: (1) to identify student variables directly effected on science learning achievement (2) to identify the direct influences of classroom variables and cross level interaction between classroom variables and student variables effected on student science learning achievement, and (3) To identify the direct influences of school variables and cross level interaction between school variables and classroom variables or between school variables and student variables effected on student science learning achievement.
The sample of the study employed multi-stage random sampling. It consisted of 3 groups: (1) 132 school administrators: principals, assistant principals and heads of science department from 44 public upper secondary schools in Thailand, (2) 132 science teacher who taught Chemistry, Biology and Physics in the classroom, from 88 classroom samples ( 2 classrooms per school), and (3) 2,488 Grade 11 science students.
If it’s possible, could you kindly give me some advice for these question?
1. Are the results effectiveness to report?
2. Are two classrooms per school powerful enough for employing HLM?
 Bengt O. Muthen posted on Thursday, August 10, 2006 - 6:36 pm
This sounds like multilevel modeling would work well - you have enough schools and classrooms. 2 classrooms per school is a bare minimum which does not allow you to study many classroom variables. Mplus does not currently handle this 3-level model.
 Jeff Cookston posted on Thursday, October 19, 2006 - 2:23 pm
We have a dataset that includes three waves of data collected on a number of family context constructs. LGM has been our preferred method of analysis, but we're now planning to collect 2 days of cortisol samples from our participants with multiple cortisol samples each day. Most prior studies that use cortisol data tend to model the daily hormone patterns using HLM. I'm confused how we can use our LGMs of the family context constructs to predict the HLM based hormone patterns. Could the cortisol data be modeled in LGM and then used as a dual process predicted by family context?
 Linda K. Muthen posted on Thursday, October 19, 2006 - 4:27 pm
Are you referring to HLM the program or hierarchical linear modeling in general?
 Jeff Cookston posted on Thursday, October 19, 2006 - 8:33 pm
Sorry, hierarchical linear modeling in general.
 Linda K. Muthen posted on Friday, October 20, 2006 - 8:02 am
The SEM and HLM growth models differ in two basic ways. One is the treatment of time scores. In SEM, they are treated as parameters in the model. In HLM, they are treated as data. The second is the treatment of time-varying covariates. The regression coefficients are fixed in SEM and random in HLM. Mplus can have time scores as parameters or data and can have fixed or random coefficients for time-varying covariates. So I think you should be okay.
 Frank Gallo posted on Sunday, August 09, 2009 - 8:02 pm
Dear Dr. Muthen

I am a beginner with Mplus. I am using Mplus Version 5.21. I have stratified data: police arrests (n =3,300) within police departments (n = 16) that serve community population levels (n = 4). The DV police force is continuous. I have a mixture (nominal, ordinal, ratio) of 21 covariates at level 1 and none at levels 2 and 3. Community levels are fixed effects. Would the multilevel modeling features of Mplus handle these data? Thank you.

Best regards,
Frank
 Linda K. Muthen posted on Monday, August 10, 2009 - 6:44 am
It sounds like you have a two-level cross-sectional model which can be estimated in Mplus. The problem I see is that you have only 16 police departments. It is usually recommended to have a minimum of 30 clusters.
 Utkun Ozdil posted on Thursday, December 16, 2010 - 11:28 am
Hi,,

I collected my data from a university's three faculties (Faculty of Education, Faculty of Engineering, and Faculty of Arts and Sciences). In each of these faculties were involved second, third, and fourth grade undergraduates. So, I have students nested within grade levels within faculties. This led me to analyze a three-level model.
Does MPlus handle such data analysis as mine or is the HLM program more appropriate?

Thanks...

Utkun
 Linda K. Muthen posted on Thursday, December 16, 2010 - 2:49 pm
Mplus does not currently have three-level cross-sectional models. HLM does. Your data, however, are not suitable for multilevel modeling given that faculty and grade cannot be considered random modes.
 Jing Zhang posted on Wednesday, August 24, 2011 - 3:35 pm
Dear Dr. Muthen,
In your post dated on March 26, 2002, you talked about how to deal with 3-level modeling of growth of students within schools. You said that level 1 and level 2 are combined into the "Within" part of the model by viewing the level 1 across-time variation as a multivariate observation vector rather than as a univariate repeated observation. My question is that:
Does this mean that the data in long format will not work, and the data has to be changed to wide format if it is in long format?
Thanks,
Jing
 Linda K. Muthen posted on Wednesday, August 24, 2011 - 5:07 pm
Yes.
 Andrea M Reina Tamayo posted on Monday, September 22, 2014 - 8:12 am
I am working on a three-level CFA model (unbalanced data). The method I used was ESM to examine the variability of a continues variable. Because the method is so intense, I used three items to capture the construct.
Person gave ratings on these items three times a day, for five days. Therefore, moments were nested within days, and days within people. These are the 3 levels.

I gave a unique ID to every person, and this unique ID appears in the data 15 times per person.

Example below for one person a bit of a second person. M stands for moment.

ID Day M X1 X2 X3
1234 1 1 1 6 7
1234 1 2 2 4 6
1234 1 3 3 . .
1234 2 1
1234 2 2
1234 2 3
1234 3 1
1234 3 2
1234 3 3
1234 4 1
1234 4 2
1234 4 3
1234 5 1
1234 5 2
1234 5 3
1567 1 1
1567 1 2
1567 1 3
1567 2 1

When I run my analysis MPlus gives me a warning message:

*** WARNING
Clusters for DAY with the same IDs have been found in different clusters
for RESP_NR. These clusters are assumed to be different because clusters for
DAY are not allowed to appear in more than one cluster for RESP_NR.

I want to know what does this warning message mean? Can I trust my output with it, or is it affecting my results?
I would appreciate your help!
 Linda K. Muthen posted on Monday, September 22, 2014 - 9:39 am
Please send the full output and your license number to support@statmodel.com.
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