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Anonymous posted on Friday, March 11, 2005  10:43 am



Dear Professor Muthen, I have some questions about the path analysis. (1) I tried your example 3.11 first. The original code is model: y1 y2 on x1 x2 x3; y3 on y1 y2 x2; Question (1) is: are these x1 x2 x3 assumed correlated in the first regression by default? (2) Then I tried with model: y1 y2 on x1 x2 ; y3 on y1 y2 x2 x3; x1 with x2; Question (2) is: In the output, I got x1 with x3, x2 with x3 also. But those are not what I specify in the model. What is it going on here? I met the similar situation with other data, when I specify one variable with another in the model, I got a lot of other "with" in the oupput. Question (3) is: How can I specify x1 is correlated with x2, x1 is independent of x3? (3) Finally, I tried with, model: y1 y2 on x1 x2 ; y3 on y1 y2 x2 x3; x1 with x2; output: modindices; So, in the output I got some "with" modifications. Question (4) is: How does this option work? Add one path per time? How can I specify the suggested "with" modification in the model? Thanks for your time! 


1. As in regular regression, the model is estimated conditioned on the x's. 2. When you mention x1 WITH x2, they are no longer treated as exogenous variables. Therefore, you no longer estimate the model conditioned on x1 and x2 but there are part of the model. You should not mention x variables in the MODEL command except on the right hand side of ON. 3. You will obtain modification indices for all parameters that are fixed or constrained to be equal to other parameters. See the SEM literature for how to use modification indices. See the Mplus User's Guide for a description of them. 

Anonymous posted on Tuesday, March 15, 2005  10:09 am



Thanks for your quick answers. Another question is can I use Mplus to fit the path analysis model with "feedback loop", i.e. X and Y are reciprocally causing each other? Thanks. 


Yes. 

Anonymous posted on Sunday, April 03, 2005  7:33 pm



Could you show you how to write the code for the path analysis with "feedback loop"? Thanks. 


y1 ON y2; y2 ON y1; 

Reetu Kumra posted on Thursday, April 13, 2006  1:16 pm



Hi, I have three imputed datasets from NORM that I am working currently working with. I ran the exact same model for all three datasets. It seems as though MPlus added on a few 'with' statement that aren't specified by me. These statements aren't the same in the three outputs I am looking at. Why exactly does this happen? Thanks, Reetu 


I would not be able to tell you that without more information. If the inputs are identical and only the data set name changes, I would be surprised to see different defaults in effect. If you want me to look at this, send the input, data sets, outputs, and license number to support@statmodel.com. 


I realized where my error was. There was one variable in the 'use variable' statement that was located in a different spot than in the other use variable statements. Which raises my next questions: 1. Why would that make a difference in the with statements that are produced? 2. Why are the additional with statements that aren't prespecified on the output? Thanks for your help! Reetu 


I cannot answer your question without the information that I asked for above. 


Sorry if I've posted this message under the wrong topic. I wasn't sure where to post it. I really like being able to run multiple regression models using MPLUS with FIML since it avoids listwise deletion. 1. Is there a way to get a plot of the residuals (estimated value of dependent observed variable minus actual value of dependent observed variable vs the predicted (estimated) values? This is very useful to check whether the model should be linear or quadratic. 2. Is there a way to see the Variance Inflation Factor values to check for problems with multicollinearity? 


1. Individual residuals are not automatically available in Mplus. You can use the DEFINE command to create them. 2. No. 


Thanks for your answers, Linda. Another reason I was interested in the plot of individual residuals is that it reveals whether heteroscedasticity is a problem. I have one book on multiple regression that says when the homoscedasticity assumption is violated "conventionally computed confidence intervals and conventional ttests of OLS estimators can no longer be justified." I don't know whether this warning is applicable when the multiple regression coefficients are estimated in Mplus using FIML. 1. Should I be concerned about the potential for heteroscedasticity when using FIML with the ML estimator? 2. If I use FIML with estimator = MLR so that robust standard errors are generated? 3. If the negative consequences of heteroscedsasticity are as likely/severe using FIML as in conventional OLS multiple regression, how would you recommend I check for heteroscedasticity using Mplus? Your guidance is greatly appreciated! 


The sames issues related to heteroscedasticity apply to both OLS and ML. See Example 3.9 in the user's guide for a suggestion with how to deal with this. 


Thanks for the very quick reply, but I could use a little more information regarding my second and third questions: Do the robust standard errors from the MLR estimator provide any protection against the negative consequences associated with heteroscedasticity? How would you recommend I check for heteroscedasticity in a multiple regression using Mplus? Again, your assistance is much appreciated. 

Toan Huu Ha posted on Wednesday, April 01, 2009  5:24 am



Dear Dr. Muthen, I run the path analysis in Mplus and got the result for chi square like this ChiSquare Test of Model Fit for the Baseline Model Value 920.454 Degrees of Freedom 58 Value 0.0000 Can you kindly let me know why the chi square test is so high. My sample size is 335 cases. Thank you for your kind response. I really appreciate that 


You have a lot of degrees of freedom. I would look at modification indices to see where the model misfit is. Use the MODINDICES option of the OUTPUT command. 


Calvin Croy: MLR protects against heteroscedasticity. See: White (1980). A heteroscedasticityconsistent covariance matrix estimator and a direct test for heteroscedasticity. Econometrica,41, 733750. One way to test for heteroscedasticiy is to compare the ML and MLR standard errors. You can also do the procedure suggested in Example 3.9. 

Toan Huu Ha posted on Wednesday, April 01, 2009  10:47 am



Thank you so much. I got the model fixed. 


Dear Prof. Muthén, I have conducted a path analysis with two independent and four dependent variables (using means and sum scores). Since I have hypotheses about the direction of the influence from the independent on the dependent variables it would be appropriate to report the onetailed pvalue. However, Mplus only computes the twotailed pvalues. Is there a possibility to obtain the onetailed pvalue using a specific outputcommand? Or is it sufficient to divide the twotailed pvalue by two? Is it appropriate to restrict some of the intercorrelations between the dependent variables using the WITHstatement due to content aspects? (one dependent variable is measured via video analysis and therefore no correlations are expected with the other 3 dependent variables). Thanks for your help. Tony 


To obtain the onetailed pvalue, look up the z value in a z table. A path model should reflect the presence and absence of relationships based on theory. If theory suggests a relationship is zero, it should be fixed at zero. 


Hello, I want to accompany a correlation matrix with my longitudinal path model. Mplus output gives correlation coefficinets among variables used in the models, but how do I get significance levels of these correlations? In SPSS, the correlations are different because the program uses listwise delition (which I don't want). Thank you, Kristine 


It would be complicated to do this in Mplus given that the covariance matrix is analyzed for path models not the correlation matrix. You would have to use WITH statements to define all covariances and then use MODEL CONSTRAINT to turn them into correlations. 

Qilong Yuan posted on Monday, April 19, 2010  12:34 pm



Hi, My model specification is this: y2 ON y1; y3 ON y2; x2 ON x1; x3 ON x2; y2 ON x1; y3 ON x2; x2 ON y1; x3 ON y2; y1 WITH x1; But in addition to all of these paths, I also get an estimate of “x3 WITH y3”. When I remove “y1 WITH x1” the correlation between x3 and y3 is still estimated. I am surprised to get a correlation I did not specify. This is a correlation between disturbance on x3 and y3, correct? Is it essential to the model, or would it be reasonable to fix it to zero (and gain a degree of freedom)? 


Mplus estimates certain parameters as the default. If you don't want them, fix them to zero, for example, x3 WITH y3@0; 


Hello I am running path models where: Y1 on X1 which gives me all the usual fit statistics. On the other hand, when I use type=missing, no chisquare statistics or CFI/TLI values are computed. In addition when I add more variables such that Y1 ON X1 X2 X3... The chisquare value and CFI/TLI are not calculated (but I don't get any error messages either). I only see LL, AIC, BIC and SRMR for model fit. How can I get MPLUS to calculate the chisquare and CFI/TLI values? These are not my full models but I need to run them before I start specifying my full path model. 


You are using an old version of Mplus where you need to specify TYPE=MISSING H1; to get chisquare and related fit statistics. 


Thank you. How about when running a multilevel path model? (Estimator = ML, Integration=Montecarlo) Even if I type Type=Missing H1 I do not get the chisquare and related fit statistics. 


With numerical integration, chisquare and related fit statistics are not defined. 

Carri Hand posted on Wednesday, October 13, 2010  9:29 am



Dr. Muthen, I ran a 2 group path analysis using the grouping command. How can I constrain the path coefficients to be equal in each model, and can I request a modification index for these? Thank you 


See the user's guide under Multiple Group Analysis  Special Issues. Then see Equalities in Multiple Group Analysis. Use the MODINDICES option of the OUTPUT command to obtain modification indices. 


I have some questions regarding defaults for correlations among predictor variables in a path analysis. Using example 3.11, the model statement is (y1 y2 ON x1 x2 x3; y3 ON y1 y2 x2;). According to the figure, the 3 correlations between x1, x2 and x3 are also estimated, which leads me to believe that the correlations among the predictors are estimated by default. These correlations, however, are not reported in the output and are not reflected in the number of free parameters. If I change the model statement to also include the correlations (x1 WITH x2; x1 WITH x3; x2 WITH x3;), 9 additional parameters are estimated (the 3 correlations, 3 means and 3 variances for x1, x2 and x3). All parameter estimates, standard errors, intercepts and residual variances that overlap in the two output files are identical. In addition, the chisquare tests, CFI, TLI, RMSEA and log likelihood are also identical. The AIC, BIC and Adjusted BIC change, however, due to the increase in the number of free parameters. Hence, is the first model statement estimating all of these parameters behind the scenes but not reporting them or including them in the number of free parameters? Or are these theoretically different models? That is, does adding the correlations for x1, x2 and x3, result in correlating the residual rather than correlating the observed variables of x1, x2 and x3? Any help or clarification is much appreciated. Thank you. 


The arrows in the diagram show that these covariances are not fixed at zero during model estimation. A regression model is estimated conditioned on the observed exogenous variables. Their means, variances, and covariances are not model parameters. When you include them in the model, you treat them as dependent variables and make distributional assumptions about them. In the case of all continuous variables and no missing data, the two approaches have the same results. When you move away from this situation, you will see differences in the results. 


Thank you, Linda. This makes perfect sense now. I didn't realize the arrows denoted the default for model parameter estimation. I was under the assumption that the arrows among the predictors had to denote correlated residuals, since as you stated the correlations, variance and means of the predictors are not estimated as model parameters. Thank you for the clarification. 


Dear Drs. Muthén I am running a path analysis with ordinal observed variables (both exogenous and endogenous). I know that in MODEL RESULTS, the "WITH" function renders residual covariance, but I have three questions: 1. What kind of estimate is calculated between pairs of endogenous variables in the RESIDUAL OUTPUT? i.e. Model estimated Covariances, Correlations or Residual correlations? 2. Are the errors for such estimated Covariances/ Correlations/ Residual correlations, the same errors (S.E.) for their corresponding covariance/residual covariance in MODEL RESULTS? 3. If the previous answer is NO; How can I obtain such errors? Thank you. 


1. It is modelestimated covariances/correlations, not the residual versions. 2. No 3. Only way is to express these estimates in Model Constraint which then gives the SEs automatically. 


Dear Dr. Muthén. Thank you for your quick answer. Regarding my message of August 20, 2012  10:10 am; some additional questions: 4. The endogenous variables are regressed on other variables (exogenous and endogenous, some common to both variables); thus, is the modelestimated correlation a part (semipartial) correlation? 5. Under which situation, will a residual correlation be estimated? Thank you. 


45. Modelestimated correlations are always regular correlations (not semipartial). But if you have observed covariates, the correlations are conditional on the covariates. 


Dear dr. Muthén. I am working with Mplus v. 4.2. I read the manual and I could not realize how to express model correlations between dependent categorical variables with the Model Constraint function. Please, how can I do that? Thank you. 


See an SEM book like Principles and Practice of Structural Equation Modeling by Rex Kline to find the formulas you need. Then label the parameters you need to express those formulas in the MODEL command and use the labels in MODEL CONSTRAINT to express those formulas. 


I am a new user. I have done a path analysis with six factors. Estimator analysis is MLM. The correlations between factors, are pearson or Spearman?. Mplus correlations are different of correltion calculated with SPSS, is this possible? It the answer is yes, What´s happening? If the answer is no, Where is the mistake? Thank you! 


The results show covariances. The standardized solution shows Pearson correlations. 


Dear Linda, Thank yor for the answering. So, In my data, the correlations with sPSS and MPLUS outdata aren´t different. Could you tell me what I should review? Tnak you! 


I don't understand your question. Please send relevant outputs and your license number to support@statmodel.com. 


Dear Linda, I have just solved my problem. Data were wrong. Thak you for your help 


Hi Linda, I am running two different path models and for several variables I am getting 999.00 values under the standardized residuals and the modification indices sections. I can see from other posts that this is likely due to a zero denominator but that this does not reflect poorly on the model. Is this correct for both? Also, modification index statements are all ON statements. I realize this means regressed on but in the context of MI, what is this telling me about these variables? In addition, As these are path models and I'm using single indicators (subscale scores), is it advisable to fix an an error variance for some predetermined value for these indicators? Thank you. 


You ask 3 questions; here are the answers: 1. Yes 2. The ON statement refers to a parameter that is restricted (fixed or held equal to another parameter) and freeing it will give a better chisquare for the model. 3. Typically not. Only if you have very good data on its reliability. 

Cecily Na posted on Monday, July 29, 2013  6:55 pm



Hello Professor, I have a simple path model. a b c ON e f g; Why does the model output show estimates of a with b a with c b with c Why does the program assume errors of endogenous variables covary? Thank you. 


This Mplus default is chosen because such residual covariances among DVs are most often needed. If it was not the default, some users may overlook this fact. It is easy to avoid the default by saying e.g. a with b@0. 


Dear Linda, I conducted a path analysis to understand direct effect of X (binary) on Z (continuous) and indirect effect of X on Z through a mediating variable Y (binary). My question is silly  I wonder how to calculate variance in Z which was explained by X and Y, respectively? Thank you. 


If your mediator (y) was continuous the variance components of your distal (z) would be beta^2*gamma^2*V(x)+ beta^2*V(e1) + V(e2) where beta is the slope in z on y, gamma is the slope of y on x, e1 is the residual in y on x, and e2 the residual in z on y. So the second term is the contribution by y. But for your mediator to be continuous you would have to consider a continuous underlying latent response variable for y using WLSMV. Better ways to handle a binary mediator are described in the paper on our website: Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. 


Dear Linda, Thank you  the formula for mediators (continuous variables) as you described above is clear to me. After taking a look at the technical report, I am still not clear about how to calculate variance in Z (continuous variable) which was explained by X and Y (both x and y are binary variables), respectively. Is it possible you can explicitly describe the formula to help us calculate? Than you. 


The causal effect literature that my paper gives a survey of does not focus on variance explained but instead indirect and direct effect estimates. 


If I run a path analysis Model A separately for 3 outcomes, y1, y2, y3; how come the output is different from Model B when I do them all at once? Model A: y1 on x1 x2 x3; x3 ON x2 x1; x2 ON x1; Model B: y1 y2 y3 ON x1 x2 x3; x3 ON x2 x1; x2 ON x1; In both types of analysis, the y variables have the same endogenous paths, so how come when multiple y variables are in the same model all the estimates change? (all variables are binary) 


It seems you are using the WLSMV estimator. The results with differ with WLSMV because the sample statistics for model estimation are a set of probit regression coefficient and residual correlations. These will differ when you do the analysis one equation at a time or all at the same time. 


Thank you very much for your advice. I'm actually using ESTIMATOR=MLR; INTEGRATION=MONTECARLO; Would this apply in a similar way? (nb: the results are qualitatively quite different from each other) 


Please send the outputs and your license number to support@statmodel.com so I can see exactly what you are doing. 


Hello, I am using the indirect command for a path analysis using observed continuous variables. I am finding the total and indirect estimates are 0 and the S.E.'s are 0. I am wondering why might this occur? Thanks so much for your time. 


The indirect effect may not be part of your model. Draw your path diagram and check. See MODEL INDIRECT in the user's guide also. 


I am running a crosslagged path model of two variables (er and hp) with repeated measures over three time points (all observed, all continuous), and correlated within each time point er2 on er1 hp1; hp2 on er1 hp1; er3 on er1 hp1 hp2; hp3 on hp2 er1 er2; er1 with hp1; er2 with hp2; er3 with hp3; In a path model with observed variables, it is necessary to allow the residual of the endogenous variables of each variable to covary to account for shared method variance across the time points? 


No, it is up to you and modification indices to decide. 


Dear linda, I have done the following code to run path analysis: TITLE: This is an example of path analysis with a combination of continuous and categorical DATA: FILE IS 'F:\Policy 138\Mplus\Company_B_Coded.NV.txt'; VARIABLE: NAMES ARE y x1x13 u1u6; USEVARIABLES ARE y u1 x1 x2 x3 x4 x9; NOMINAL ARE u1; MODEL: u1 ON x1 x2 x3; y ON u1 x1 x2 x3 x4 x9; Here I have y (dependent variable) is continuous, u1 (in between variable) is unordered categorical (nominal), x1 is continuous exogenous, x2 and x3 are binary, x4 and x9 are unordered categorical (nominal). I received the following error: ERROR in MODEL command ‘A nominal variable may not appear on the righthand side of an ON statement: U1’ Could you help me, please? I have to show the results tomorrow. 1 How can I solve this problem? 2 Do I need to define x4 and x9 as nominal variables as well? If not how the program will know that they are categorical nominal variables? 3 How can I save the results in a word document? 4 How can I save the diagram in a word document? Your help is really appreciated. Apologize if I asked a lot? Thanks in advance. 


You can't use a nominal variable as a mediator. 


Thanks Linda, To solve this shall I transfer this nominal variable to some binary variables or what can I do else? Could I ask you to refer to my question number 2, please? Walaa 


1. The easiest approach is to change the nominal mediator to a binary mediator (you can do several analyses with different cuts). A more advanced approach, not for beginners, is shown in my 2011 mediation paper Muthén, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. Click here to download the paper. Click here to view the Technical appendix that goes with this paper and click here for the Mplus input appendix. Click here to view Mplus inputs, data, and outputs used in this paper. 2. If an x variable is nominal (that is, has several unordered categories), you need to split it up into C1 binary dummy variables (where C is the number of nominal categories). 


Many thanks indeed! I downloaded your paper and I will do my best to understand it and apply this in my model. In fact, I want the mediator to be a nominal variable. 

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