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I am working on a 2level path analysis to study travel behavior of individuals (level 1) within neighborhoods (level 2). The dataset consists of information of singles, so there is no interaction with a householdlevel. This is how I defined the model: DATA: file is C:\single.dat; VARIABLE: names are ...; usevariables are ...; within = age sex driv_lic degree employed car income weekend; between = dist_pt pop road housing com entropy; cluster = neigh; ANALYSIS: TYPE = TWOLEVEL; MODEL: %WITHIN% distance ON age sex driv_lic degree employed car income weekend; time ON distance age sex driv_lic degree employed car income weekend; %BETWEEN% distance on dist_pt pop road housing com entropy; time on distance dist_pt pop road housing com entropy; MODEL INDIRECT: time ON distance age ... However, I get this error: *** ERROR The number of observations is 0. Check your data and format statement. Data file: C:\single.dat *** ERROR Invalid symbol in data file: "age" at record #: 1, field #: 3 I checked the datafile, but I can not find out what goes wrong. Thanking you in advance, Veronique 


It sounds like you have the variable names as the first record of your data file. You need to remove the record that contains the variable names. 


Hi, I am running a twolevel path model (with fixed slopes but random intercepts). I have tried to use different centering options for withinlevel covariates (grand and groupmean centering). I understand that these transformations should affect the intercept values. But my slopes (and their significance) change dramatically as well. How can this be? I have understood that this should not be the case (as I don't have random slopes). 


Grand mean centering will result in the same regression coefficients as no centering because the same value is subtracted from each value of the variable. Group mean centering will result in different regression coefficients because different values are subtracted from each value of the variable depending on the cluster. See Table 5.11 on page 140 of Raudenbush and Bryk shows this. 


Thank you for your quick reply. However, I guess there is still a slight difference in parameters (slope coefficients) when using raw vs. grandmean centered variables. For instance, under no centering: ARITM2 ON READING0(B = 0.016; SE = .027) ARITM2 ON MATH0 (B = 0.031; SE = 0.011) ARITM2 ON AVOID0 (B = 0.104; SE = 0.050) But when I grandmean center, ARITM2 ON READING0(B = 0.059; SE = 0.027) ARITM2 ON MATH0 (B = 0.036; SE = 0.011) ARITM2 ON AVOID0 (B = 0.064; SE = 0.046) What is the reason for that? Also, why does the model fit change? 


There should be no differences. The fit should be the same. If the fit changes, then either you are hitting a local solution in one case or the centering is not the only difference between the two models. For further information, please send the two outputs and your license number to support@statmodel.com. 


Hi, I might send my outputs. But I also already checked it and it seems that you are correct about hitting a local solution. It concerns the model where raw scores are used. Thus, I might use grandmean centered scores then. RANDOM STARTS RESULTS RANKED FROM THE BEST TO THE WORST LOGLIKELIHOOD VALUES Final stage loglikelihood values at local maxima, seeds, and initial stage start numbers: 3830.482 unperturbed 0 3831.864 93468 3 3831.864 27071 15 3831.867 259507 53 3831.867 565819 65 3833.319 761633 50 4 perturbed starting value run(s) did not converge. WARNING: THE BEST LOGLIKELIHOOD VALUE WAS NOT REPLICATED. THE SOLUTION MAY NOT BE TRUSTWORTHY DUE TO LOCAL MAXIMA. INCREASE THE NUMBER OF RANDOM STARTS. 

Kätlin Peets posted on Wednesday, February 09, 2011  2:33 pm



I have one more question. When I use raw or grandmean centered predictors that are specified at both levels (within and between), are the betweenlevel effects already contextual effects? That's what I understand from Raudenbush and Bryk. However, in their example, they use an aggregate variable that is observed rather than latent. 


I think this is the case. See the following paper which is available on the website for further information: 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 grouplevel effects in contextual studies. Psychological Methods, 13, 203229. 

Kätlin Peets posted on Thursday, February 10, 2011  1:01 pm



I am still a bit confused. In the user's guide (p. 242), it seems that contextual effects are computed by gamma01  gamma10. This would mean that betweenlevel effects are not directly contextual effects. 


Page 242 talks about the case where you work with a latent x variable. On top of page 243 we state that using a latent x implies latent groupmean centering  so corresponding to the left column of R & B's Table 5.11. With a manifest x, grandmean centering leads to a contextual effect coming out directly as the betweenlevel slope, as in the right column of Table 5.11, and as you said. 

Kätlin Peets posted on Thursday, February 10, 2011  1:57 pm



OK. Thanks a lot. 

Jing Zhang posted on Thursday, May 03, 2012  10:57 am



I have a crosslevel mediation model or a twolevel path model with: X (independent variable at cluster level) M1 (mediator 1 at individual level) M2 (mediator 2 at individual level) Y (dependent variable at individual level) Can I use the command “IND” to examine the indirect effects from X to Y in this case? I looked into the Mplus forum, notes and other related website of Mplus, it seems to me that “IND” is used with onelevel model only in the examples I have found. Is there a reason that “IND” is not used in a twolevel path model? 


MODEL INDIRECT is available with TYPE=TWOLEVEL. 


I was wondering if I am able to analyze a 2level path model that is a linear path where X is a Level 2 variable, the two mediators (M1 and M2) are Level 1 variables, and the dependent variables is a Level 1 variable. The model looks like this: SPP(Level 2) > ns_comp (Level 1) > exp_mean (Level 1) > lonely (Level 1) I tried to run the model using the syntax below; however, I get a warning that says "Variable on the lefthand side of an ON statement in a  statement is a WITHIN variable. The intercept for this variable is not random. Variable: EXP_MEAN" Usevariables = SOP SPP ns_comp exp_mean lonely; Useobservations = Surveys gt 14; MISSING = ALL (999); within = ns_comp exp_mean; between = SPP SOP ; Cluster = ID; DEFINE: center spp sop (grandmean); Analysis: Type = twolevel random; ALGORITHM=INTEGRATION; INTEGRATION=MONTECARLO; Model: %within% s  exp_mean on ns_comp; s2  lonely on ns_comp; %between% s on SPP SOP; s2 on s; Does this mean the model is not executing properly? Thank you! 


It sounds like you've put exp_mean on the Within list. This contradicts having this variable on the lefthandside of a random slope statement  if you say that the slope varies across between units, the variable varies across between units and is therefore not a Within variable. Note that you don't have to have random slopes (they are often not random). 


Hi Dr Muthen, Is it possible to predict level 2 dependant variable with level1 independant variable and level 1 mediator? I think of using the following syntax with Two Level Random using examples from 9.1 onwards %WITHIN% S m on x; %BETWEEN% m on x (a); y on m (b) S (c); Model constraint: New (indirect); Indirect= a*b; 


You can say %WITHIN% S m on x; %BETWEEN% m on x (a); y on m (b) x (c); s on x; s with y m; Model constraint: New (indirect); Indirect= a*b; The best approach is to use Estimator = Bayes; see the new paper on our website: Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and timeseries models. Technical Report, Version 2. August 5, 2018. Accepted for publication in Structural Equation Modeling. (Download scripts). 


***ERROR in MODEL command Unrestricted xvariables for analysis with TYPE=TWOLEVEL and ESTIMATOR=BAYES must be specified as either a WITHIN or BETWEEN variable. The following variable cannot exist on both levels: X This error command appear. 


Same problem occured to me. If I restrict X to within level, then I could not test "c" path and hence could not infer about partial or full mediation. 


Are you using version 8.1? If so, send output and data to Support. 


I am using version 8. Is this feature npt available on 8? 


Latent variable decomposition for an X with random slope using Bayes was introduced in Version 8.1  see the Version History page on our website: http://www.statmodel.com/verhistory.shtml 


Perfect, Thank you. 

Jason Lava posted on Saturday, September 01, 2018  8:52 pm



Hi Dr Muthen, I read this article you mentioned and saw the initial discussion. It looks great. What I get is that we can now test 112 model where outcome has no within cluster variation. Right? If I am correct, then this is a big thing since it was a limitation in earlier multilevel models. 


The new feature is for random slope situations. We already did 112 models without random slopes where outcome has no within cluster variation. 


Use variables are Independent, Mediator, Dependant; Between= Dependant; Within= Independent; Cluster= Team ID; Analysis: Type= TWOLEVEL RANDOM; Estimator=Bayes; Model: %WITHIN% Mediator ON Independent (a); %BETWEEN% Dependant ON Mediator (b); Model Constraint: New (Indirect); Indirect= a*b; My question is how can I estimate Independent (Level 1) to dependant path (Level 2)? 


Sounds like yet another variation on your mediation theme. In this case, I would delete the Independent variable from the Within= list and add on %Between% Mediator on Independent (a); and delete your within level "(a)". In this way, it is the betweenlevel part of Independent that influences the betweenlevel part of the Mediator which in turn influences the Dependent variable, resulting in the indirect effect a*b. 


Thank you. One final question, do we need to test a*b and c in ONE model or test them separately? If I test them separately, all paths are significant including the a*b indirect effect. When test them in a ONE model, everything becomes insignificant. Can you please advise on this? 


They should be tested separately. They are different hypotheses. 

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