It is a pity because you can always enjoy more optimistic results with alignment as compared to the conventional frequentist, exact measurement invariance techniques.

In this post I summarized, in an approachable way, the steps that are necessary to apply alignment procedure. Intro Step 1. Find an acceptable configural invariance model Step 2.

Next goes one or some of the following:. It will also provide approximate latent means, even if there is no exact measurement invariance. If you believe the model is likely to be invariant, but your data are noisy i. One sign to apply approximate approach is when you experience problems even with configural invariance model but you are sure your model is properly specified.

If you believe that most parameters are invariant AND your data are noisy, there is an option of Bayesian alignmentwhich combines approximate invariance with alignment approach. I describe it in section 8. You may speculate about differences in meaning, make cognitive interviews to understand it, or apply multilevel CFA with a group-level covariate as in Davidov et al. Below, I focus on alignment method in Mplus software.

Alignment estimates a configural invariance model and then modifies the factor loadings and intercepts to make them as similar as possible without deteriorating the model fit. Conceptually, the procedure is alike target factor rotation where the target is across-group similarity of loadings and intercepts. If the fit of configural model is not good enough, consider fitting the configural model using Bayesian approach and testing approximate Bayesian invariance probably with further alignment.

Dropping items and groups are the hardcore measures, apply them only if it is reasoned substantively. My example: I have a data from World Values Survey wave 5 on 10 countries the sample was randomly shrunk to respondents for the speed of computation. The model is a single factor of sexual and reproductive morality. It has 4 indicators: justifiability of homosexuality, prostitution, abortion, and divorce.

The residuals of abortion and divorce are allowed to covary.We are continuously improving the tutorials so let me know if you discover mistakes, or if you have additional resources I can refer to.

The source code is available via Github. The data we will be using for this exercise is based on a study about predicting PhD-delays Van de Schoot, Yerkes, Mouw and Sonneveld The data can be downloaded here. Among many other questions, the researchers asked the Ph. It appeared that Ph. For more information on the sample, instruments, methodology and research context we refer the interested reader to the paper.

### WAMBS Mplus Tutorial

The relation between completion time and age is expected to be non-linear. This might be due to that at a certain point in your life i. Although it is a. Once you loaded in your data, it is advisable to check whether your data import worked well. Therefore, first have a look at the summary statistics of your data.

You can do this by looking at the sampstat ouput. Before actually looking at the data we first need to think about the prior distributions and hyperparameters for our model. For the current model, there are four priors:. Next, we need to specify actual values for the hyperparameters of the prior distributions.

It is a good idea to plot these distribution to see how they loo and waht expected delay would be given these priors. To see what default priors Mplus uses we can have a look at the Appendix A of this manual. Be careful the actual density you see, is the density of the posterior, the prior is summarized in the different coloured lines.

This seems to be a bit of a bug in Mplus. As an example the prior distribution of the regression coefficient for age. By default Mplus discards half of the iteration as burnin period. Clearly, two times 50 iterations is not enough for obtaining trusthworthy results and we need more iterations. Inspect the traceplots again. It seems like the trace caterpillar plots are neatly converged into one each other we ideally want one fat caterpillar. This indicates we already have enough samples.

We can double check check if the chains converged by having a look at the convergence diagnostics, the Gelman and Rubin diagnostic. Is this the case?. The PSRF for all iterations after burn-in is close to 1, so convergence seems to have been reached.

As is recommended in the WAMBS checklist, we double the amount of iterations to check for local convergence. To this by changing this part of the input. In order to preserve clarity we just calculate the bias of the two regression coefficients. You should combine the relative bias in combination with substantive knowledge about the metric of the parameter of interest to determine when levels of relative deviation are negligible or problematic.

For example, with a regression coefficient of 0. The specific level of relative deviation should be interpreted in the substantive context of the model.Mplus requires data to be read in from a text file without variable names, with numeric values only, and with missing data coded as a single numeric value, such as A common workflow for preparing data to analyze in Mplus is to perform the variable cleaning in SPSS and then save the data as a text file.

These data do not include any missing values, but if they did we could easily convert all variables to have missing coded as In the new dialog box, select System-missing under Old Value.

Enter in the Value field under New Value. Click Add so that you see the following:. Next, uncheck the box next to Write variable names to file. Finally, enter the name for the new data file, such as sem-bollen. You should see the following:. Without one final little adjustment, Mplus will not correctly read the data. To see this, open Mplus. From inside Mplus, open the data file.

By default, Mplus will only look for files with a. In the lower right, next to the File name field, change to All Files. You will now see the data file with the. You can now open the file. When you do so, you will see an odd set of characters at the very start of the file highlighted here.

Now your data are ready. Then return to Mplus and paste in the values. Mplus requires that you type out the names in the order in which the columns appear in the data file. This will place them in the correct order. The following runs the model:.

From SPSS Mplus requires data to be read in from a text file without variable names, with numeric values only, and with missing data coded as a single numeric value, such as First, open the data file in SPSS.

You should see the following: These data do not include any missing values, but if they did we could easily convert all variables to have missing coded as The data are now ready to be saved.You are interested in studying drinking behavior among adults.

Rather than conceptualizing drinking behavior as a continuous variable, you conceptualize it as forming distinct categories or typologies.

For example, you think that people fall into one of three different types: abstainers, social drinkers and alcoholics. Since you cannot directly measure what category someone falls into, this is a latent variable a variable that cannot be directly measured.

However, you do have a number of indicators that you believe are useful for categorizing people into these different categories. Using these indicators, you would like to:. Example 2.

High school students vary in their success in school. This might be indicated by the grades one gets, the number of absences one has, the number of truancies one has, and so forth. A traditional way to conceptualize this might be to view "degree of success in high school" as a latent variable one that you cannot directly measure that is normally distributed.

However, you might conceptualize some students who are struggling and having trouble as forming a different category, perhaps a group you would call "at risk" or in older days they would be called "juvenile delinquents".

Using indicators like grades, absences, truancies, tardies, suspensions, etc. We have a hypothetical data file that we created that contains 9 fictional measures of drinking behavior. The 9 measures are. Using Stata, here is what the first 10 cases look like. Note that I am showing you results before showing you the program.

I will show you the program later. First, the probability of answering "yes" to each question is shown for each type of drinker latent class. For example, consider the question "I have drank at work". This would be consistent with the first class being alcoholics.

Looking at the pattern of responses for all classes gives you an overall picture of the meaning of the three classes that are identified and helps us create descriptive labels for the classes. We are hoping to find three classes that correspond to abstainers, social drinkers, and alcoholics. Abstainers would have a pattern that they generally avoid drinking, social drinkers would show a pattern of drinking but generally in moderation and seldom in self-destructive ways, while alcoholics would show a pattern of drinking frequently and in very self-destructive ways.

I have reformatted that output to make it easier to read, shown below. Each row represents a different item, and the three columns of numbers are the probabilities of answering "yes" to the item given that you belonged to that class. So, if you belong to Class 1, you have a By contrast, if you belong to Class 2, you have a Looking at item1, those in Class 1 and Class 3 really like to drink with Jumping to item5, I am starting to believe that Class 3 may be labeled as "alcoholics".

It seems that those in Class 2 are the "abstainers" we were hoping to find. Not many of them like to drink This leaves Class 1; might they fit the idea of the "social drinker"? They like to drink Campus health and safety are our top priorities. Get help with online courses, Zoom and more. I would like to use Mplus to perform a path analysis, a confirmatory factor analysis, or a structural equation model.

How can I access this software at UT? If your models of interest are small, the free demo version may be sufficient to meet your needs. When I open an Mplus command file and run it, it works fine.

**Mplus Path Modeling (multiple regression) (vid#6)**

When I use Save As in the File menu to save the command file under a different file name, Mplus doesn't work. What is wrong? Mplus was not specifically written for the Windows terminal server environment, so several oddities can arise when you use it in this environment. One unusual feature is that if you save a previously working Mplus command file, you must exit Mplus and relaunch it. Then your saved file should work correctly.

Note that you can modify an existing command file within Mplus without exiting the program. Also, you should be sure to save each command file before you run it through Mplus' command interpreter i. Mplus writes its output information to the user's window by default; if you want to reaccess your original command file you must open it again by using the File menu and selecting the Open option or the list of the four most recently-accessed files located at the bottom of the File menu.

The exception to this is that the variances and residual variances for latent response variables corresponding to categorical dependent variables may not be free. Parameter Default Starting Value Loadings for indicators of latent variables 1. Default settings are used to simplify the model specification. These assumptions are based on what is most commonly seen in practice.

The user can override all defaults. It is important to understand the default settings so that the estimated model is the model that the user expects. Mplus availability 2. Saving Mplus command files on the Windows Terminal Server 3. Mplus Defaults Mplus Availability Question: I would like to use Mplus to perform a path analysis, a confirmatory factor analysis, or a structural equation model.

Answer: Mplus was not specifically written for the Windows terminal server environment, so several oddities can arise when you use it in this environment. Following are the default starting values of other parameters: Parameter Default Starting Value Loadings for indicators of latent variables 1. Intercepts and thresholds of observed dependent variables are free.

### Latent Class Analysis | Mplus Data Analysis Examples

In single group analysis, means and intercepts of continuous latent variables are fixed to zero. In multiple group analysis, means and intercepts of continuous latent variables are fixed to zero in the first group and are free to be estimated in other groups. Means and intercepts probabilities of the categorical latent variable are free.

Variances of continuous latent independent variables are free.Structural Equation Modeling SEM is a very general approach to analyzing data in the presence of measurement error and complex causal relationships. The tutorial is motivated by a problem of symptom overlap routinely faced by clinicians and researchers, in which symptoms or test results are common to two or more co-occurring conditions.

As a result of such overlap, diagnoses, treatment decisions and inferences about the effectiveness of treatments for these conditions can be biased. This problem is further complicated by increasing reliance on patient-reported outcomes, which introduces systematic error based on an individual's interpretation of a test questionnaire.

SEM provides flexibility in handling this type of differential item functioning and disentangling the overlap. Scales and scoring approaches can be revised to be free of this overlap, leading to better care. This tutorial uses an example of depression screening in Multiple Sclerosis patients in which depressive symptoms overlap with other symptoms, such as fatigue, cognitive impairment and functional impairment.

Details of how MPlus software can be used to address the symptom overlap problem, including data requirements, code and output are described in this tutorial. Symptoms or test findings that are common to two or more conditions may confound diagnosis, treatment decisions and inferences about the effectiveness of treatment.

Commonly, a patient has both MS and depression and experiences a symptom, such as fatigue, that frequently occurs in both conditions. As a result, it may be difficult to determine whether the fatigue is a symptom of MS or a symptom of depression.

We use the problem of symptom overlap between MS and depression to motivate a more general discussion of structural equation modeling SEM. Note also, that the symptom overlap problem described above is more generalizable than it may at first seem.

For example, a scale measuring satisfaction with your teacher and letter grade earned in class would be expected to have some overlap. In the general setting, two or more variables might have overlapping manifestations are cross-loaded.

Thus, it might be difficult to disentangle these variables, confounding any inference about them separately. Kline [ 2 ] has written an influential introductory text on the topic of structural equation modeling SEMaccessible to an applied researcher, while Bollen [ 3 ] provides a comprehensive and thorough overview of general structure equation systems, commonly known as the LISREL linear structural relations model.

Woods et al.

## Mplus Tutorial (STAN 102)

Further, the MPlus website [ 13 ] is filled with manuals and examples to lead an applied researcher conducting SEM analysis. Our aim in this tutorial is to first provide a general background on SEM. We then provide a blueprint on how to apply each of these techniques in succession to understand and correct for diagnostic overlap of two or more conditions [ 23 ].

For each of these techniques the analyst must make a series of complex model decisions e. We provide details on a general sequence of models which can be used by working through the motivating example and using the MPlus software to show how to make such decisions based on theory and empirical evidence. Modern SEM has progressed rapidly with many new developments appropriate for other settings not discussed in this tutorial i.

Therefore, in order to give a clear overview, we focus on an important problem in the cross-sectional setting for our general discussion.

We start, in Section 2, with background information about a motivating example. This is followed, in Section 3, with a basic introduction to the SEM framework. In Section 6 we provide an algorithm for adjusting a scale to isolate the latent dimension of the intended condition under study in the original scale along with practical applications of the adjusted scale for clinical use.

Section 7 summarizes the paper. We provide the MPlus code for our example in the Supporting Information available from the journal web page. Scales representing a condition that may overlap with another condition may not be capturing the intended construct of interest. For example a depression screening scale may not accurately estimate depressed mood in a MS patient, due to overlapping symptoms of both conditions.

Researchers need reliable and accurate measures of symptoms or conditions that cannot be measured directly. Such measures that are unobserved are considered latent constructs. Unlike directly observable measures such as height or weight, researchers may not be able to measure variables such as depression directly. To measure such a latent construct as depression, we can capture indicators from a multiple item scale such as the PHQ-9 that represent the underlying construct.

These items are directly observed and in theory if we also account for additional measurement error in our construct, accurately represent the measure that cannot be observed directly.M plus. General Description. Mplus Programs.

Mplus Examples. Following are models in Ellipse B that can be estimated using Mplus: Regression mixture modeling Path analysis mixture modeling Latent class analysis Latent class analysis with covariates and direct effects Confirmatory latent class analysis Latent class analysis with multiple categorical latent variables Loglinear modeling Non-parametric modeling of latent variable distributions Multiple group analysis Finite mixture modeling Complier Average Causal Effect CACE modeling Latent transition analysis and hidden Markov modeling including mixtures and covariates Latent class growth analysis Discrete-time survival mixture analysis Continuous-time survival mixture analysis Observed outcome variables can be continuous, censored, binary, ordered categorical ordinalunordered categorical nominalcounts, or combinations of these variable types.

Most of the special features listed above are available for models with categorical latent variables. The following special features are also available: Analysis with between-level categorical latent variables Test of equality of means across latent classes using posterior probability-based multiple imputations Plausible values for latent classes Modeling with Continuous Latent Variables.

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