Multilevel regression
Message/Author
 Suk-Hyang Lee posted on Sunday, March 19, 2006 - 3:30 pm
Dear Dr. Muthen

I am working on data analysis for my dissertation. Multilevel regression is used for data analysis. While working on data analysis using Mplus, I got this error message.
I tried to solve this problem by increasing start value but it did not work. Would you mind if I ask your advice to solve this problem?
I look forward to hearing from you.
Below is output that I had.
Thank you in advance for your help.

INPUT INSTRUCTIONS

TITLE:
Level2 Predictors: F5

DATA:
FILE IS Study2.Mplus.Addmean.031706.dat;

VARIABLE:
NAMES ARE ID gender disabli subject OverSup LenSup
SDgroup ExCogrop cyclenum AcaResp AcaResp1
CmpResp TeInstBe F4 F5 F6 F7 F8 F9 AcsScore
AcsScf6 AcsSc6x2 blank SumSDS SumSds1 SumSds2 SumSds3 SumSds4
SumAirE SumAirS Tinsb_m Sds_Tinb checkID AcaR_m
Smag_m Comp_m Tmg_m Tfos_m F4_m F5_m F6_m F7_m F8_m
F9_m;

USEVARIABLES ARE ID F5 AcaR_m Smag_m Comp_m Tinsb_m
Tmg_m Tfos_m SumSDS;

CATEGORICAL = F5;

WITHIN = ;

BETWEEN = AcaR_m Smag_m Comp_m Tinsb_m
Tmg_m Tfos_m SumSDS;

CLUSTER = ID;

ANALYSIS:
TYPE = TWOLEVEL;

MODEL:
%WITHIN%

%BETWEEN%
F5 on AcaR_m Smag_m Comp_m Tinsb_m
Tmg_m Tfos_m SumSDS*10000.00;

OUTPUT:
TECH1 STANDARDIZED;

INPUT READING TERMINATED NORMALLY

Level2 Predictors: F5

SUMMARY OF ANALYSIS

Number of groups 1
Number of observations 1350

Number of dependent variables 1
Number of independent variables 7
Number of continuous latent variables 0

Observed dependent variables

Binary and ordered categorical (ordinal)
F5

Observed independent variables
ACAR_M SMAG_M COMP_M TINSB_M TMG_M TFOS_M
SUMSDS

Variables with special functions

Cluster variable ID
Between variables
ACAR_M SMAG_M COMP_M TINSB_M TMG_M TFOS_M
SUMSDS

Estimator MLR
Information matrix OBSERVED
Optimization Specifications for the Quasi-Newton Algorithm for
Continuous Outcomes
Maximum number of iterations 1000
Convergence criterion 0.100D-05
Optimization Specifications for the EM Algorithm
Maximum number of iterations 500
Convergence criteria
Loglikelihood change 0.100D-02
Relative loglikelihood change 0.100D-05
Derivative 0.100D-02
Optimization Specifications for the M step of the EM Algorithm for
Categorical Latent variables
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Optimization Specifications for the M step of the EM Algorithm for
Censored, Binary or Ordered Categorical (Ordinal), Unordered
Categorical (Nominal) and Count Outcomes
Number of M step iterations 1
M step convergence criterion 0.100D-02
Basis for M step termination ITERATION
Maximum value for logit thresholds 15
Minimum value for logit thresholds -15
Minimum expected cell size for chi-square 0.100D-01
Optimization algorithm EMA
Integration Specifications
Type STANDARD
Number of integration points 15
Dimensions of numerical integration 1
Adaptive quadrature ON
Progressive quadrature stages 1
Cholesky ON

Input data file(s)
Study2.Mplus.Addmean.031706.dat
Input data format FREE

SUMMARY OF DATA

Number of clusters 45

Size (s) Cluster ID with Size s

30 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16
17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32
33 34 35 36 37 38 39 40
41 42 43 44 45

SUMMARY OF CATEGORICAL DATA PROPORTIONS

F5
Category 1 0.175
Category 2 0.825

THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NON-ZERO
DERIVATIVE OF THE OBSERVED-DATA LOGLIKELIHOOD.

THE MCONVERGENCE CRITERION OF THE EM ALGORITHM IS NOT FULFILLED.
CHECK YOUR STARTING VALUES OR INCREASE THE NUMBER OF MITERATIONS.
ESTIMATES CANNOT BE TRUSTED. THE LOGLIKELIHOOD DERIVATIVE
FOR PARAMETER 7 IS -0.18718467D+02.
 Linda K. Muthen posted on Sunday, March 19, 2006 - 3:47 pm
You can try increasing the number of MITERATIONS as suggested in the error message. If that does not work, please send your input, data, output, and license number to support@statmondel.com.

Please don't post output on the discussion board. We try to keep the posts short.
 Suk-Hyang Lee posted on Sunday, March 19, 2006 - 4:58 pm
Thank you so much for your kind reply.
I am sorry to post output on this board.
I simply thought that it might be better to post it for you to understand my problem. I tried to delet it, but I could not do it. Sorry again.

I know it would be silly question.
But I am not good at Mplus, could you please let me know how I can try to icrease the number of MITERATIONS?
If there is any syntax for it, please let me know.
I hope that this question does not bother you.

Thank you for your understanding and help.
 Linda K. Muthen posted on Sunday, March 19, 2006 - 8:01 pm
Look up MITERATIONS in the Mplus User's Guide. Choose a number larger than the default value. As I said earlier, if you have further problems of this type, you need to contact support@statmodel.com and provide the information I asked for.
 Jan Hochweber posted on Wednesday, March 07, 2007 - 7:33 am
Reliability correction in regression is possible using:

f BY x@1;
x@a;
y on f;

a: err var of x; a=(1-rel)*var

My aim is to use this in ML regression with Rasch estimates as IVs on both levels. Reliability is calculated using SEs from IRT software. I'd like to apply this with A) latent decomposition of covariates and B) observed grp means and tried:

A)
%within%
f by x@1;
x@0.174;
y on f;

%between%
y on x;

x grand centered

Output: "this variable will be treated as a y-variable on both levels: x"

B)
between = xb;

%within%
f by xw@1;
xw@0.174;
y on f;

%between%
y on xb;

xw group centered, xb group mn

Comparing results of A & B with regression on LVs (2lvl Rasch), there's much higher conformity than without correction.

A)
How is the variance decomposed between levels? Is it ok to have M+ decompose the variance or should I use observed group means?

B)
With group centering, I still use x@0.174 for correction. Should I use within variance instead of total? Must reliability of grp means be taken into account (grp sizes~20)?
 Linda K. Muthen posted on Wednesday, March 07, 2007 - 10:21 am
You may find your answer in Web Note 11 at the following link:

http://www.statmodel.com/examples/webnote.shtml
 Jan Hochweber posted on Thursday, March 08, 2007 - 6:18 am
I read the web note but still need some clarification.

1) I understand that if I use latent covariates the predictor is a LV and has the "within-between status" (web note). But in the model I described (model A) regression is being done on f on lvl1 and x on lvl2. f is defined by x but is not x actually. I thought about using f as predictor on both levels but this doesn't work. I'm not sure if my model specification is correct since I use the same predictor corrected for unreliability on within (f) and not corrected on between (x).

2) In Model B I use regular group centering so predictor variance on within should be variance of deviation scores. I wonder if for the calculation of error variance I may use then:
(1 - reliability)*within variance, with reliability calculated from IRT SEs.

Thanks for your patience.
 Bengt O. Muthen posted on Thursday, March 08, 2007 - 9:08 am
I think your Model A approach is most straightforward. I would think that you get very similar results to Model A if instead you declare Within = x and use an observed between-level, centered "xb" on Between. That is similar to your B approach, although you would have to declare Within = xw and not do group centering.
 Yan Liu posted on Wednesday, November 28, 2012 - 3:28 pm
Dear Dr. Muthen,

I am working on multilevel regression analysis with random intercept only for continuous outcome variable. I have two questions.

(1) In the output, I see the variance-covariance(correlation) matrix is provided at both within- and between levels. How are the var-cov matrices computed? Are they computed like those in multilevel SEM, which are additive?

(2) Does Mplus use pseudo-maximum likelihood for multilevel regression analysis?

Thanks a lot!
Yan
 Bengt O. Muthen posted on Thursday, November 29, 2012 - 6:37 am
1. Yes.

2. What type of pseudo-ML are you thinking about? There is a pseudo-ML for complex survey data. See

Asparouhov, T. (2005). Sampling weights in latent variable modeling. Structural Equation Modeling, 12, 411-434.

and other complex survey data papers at

http://www.statmodel.com/resrchpap.shtml
 Yan Liu posted on Monday, December 03, 2012 - 11:16 pm
Dear Dr. Muthen,

Thanks a lot! That is very helpful!Just want to confirm with my about my understanding. So basically Pseudo-ML are used in Mplus if we use MLR, MLM, or MLMV estimators.
 Bengt O. Muthen posted on Tuesday, December 04, 2012 - 11:07 am
We use the term PML for type=complex or with weights.
 Li posted on Sunday, May 11, 2014 - 8:54 pm
I ran a 2-level regression with dichotomous variable as outcome. This is an intercept-only model with all the level-2 slopes fixed. Sample size is around 2,000. MPlus automatically used MLR as the estimator.

I am mostly interested in whether a level-1 predictor is significant or not. The results of the Wald test are reasonable. This predictor is significant in about 10 out of 30 cases, which agrees with the substantive knowledge. However, if I use the -2Loglikelihood difference test, this predictor is significant for all the 30 cases. I did use the scaling factor for calculating the scaled Chi-square difference. While the difference of the degree of freedom is only 1, the difference of -2 loglikelihood ratio drops by at least 200 when this particular predictor is added to the model.

I always thought Wald test and log ratio test should produce more or less equivalent results with large sample size. However, I am very confused by the drastically different results in this case. Have you ever heard of or experienced such thing? What could have gone wrong in your view? Many thanks for your comments. I really appreciate it.
Hongli
 Linda K. Muthen posted on Monday, May 12, 2014 - 9:57 am
What do you mean by 30 cases.

How many observations do you have at each level?
 Jacqueline Power posted on Friday, September 16, 2016 - 10:45 am
Example 9.1 in the manual
VARIABLE: NAMES = y x w xm clus;
WITHIN = x;
BETWEEN = w xm;
CLUSTER = clus;
DEFINE: CENTER x (GRANDMEAN);
ANALYSIS: TYPE = TWOLEVEL;
MODEL:
%WITHIN%
y ON x;
%BETWEEN%
y ON w xm;

Is xm a variable such that x multiplied by m
= xm? If this example similar to something in "Regression and Mediation Analysis using Mplus". Thank you
 Bengt O. Muthen posted on Friday, September 16, 2016 - 11:24 am
No, xm is meant to refer to the cluster mean of x.
 Hanna de Vries posted on Tuesday, September 27, 2016 - 7:37 am
Hi,

I have the following question; I want to define my constructs in mplus. HOwever, when I do this under the define command, i get errors. Is this the right place to define my constructs?

USEVARIABLE ARE L30 L31 L32 L33 L34 L39 L40 L41 L42 EMP LMX;
CENTERING IS Groupmean(emp);

Cluster = ID;

Within = EMP;

DEFINE:
Emp by L30 L31 L32 L33 L34;
LMX by L39 L40 L41 L42;

ANALYSIS:
TYPE = Twolevel random;
Estimator = MLR;

Model:
%within%
LMX on Emp;
 Bengt O. Muthen posted on Tuesday, September 27, 2016 - 8:01 am
You define constructs in the Model command, not in Define. This is because parameters are estimated related to the construct.
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