Dear Marcel, I wouldn't base the decision of the final class solution solely on the goodness-of-fit measures. Geiser (2011) recommends also to select the final class solution based on interpretability. Is the 4th class also qualitative different compared to the other classes? How are the average latent class probabilities for each latent class? If class 4 shows a value under 0.8 I personally would select a different class solution.

I really can recommend the following book: Geiser (2011). Datenanalyse mit MPlus. Eine anwendungsorientierte Einführung. Springerverlag.

Dear Josefine

what a relief. Yes, the forth groups shows significantly (tested by ANOVA and post-hoc tests, then Cohen's d) weaker self-efficacy beliefs than all other groups on all variables. That is why I would like to keep it because it stands out in stark contrast to all the others.

The latent class probalities are fine:

1. class (0,93)

2. class (0,90)

3. class (0,95)

4. class (0,91)

Large parts of my knowledge of LCA comes from said book, I find it an excellent read. However, since this is my first ever LCA, I appreciate the opinion of more experienced researchers.

Thank you very much.

Marcel

Hi Marcel,

Have a few suggestions that might help you.

It is important to realize that latent class analysis does not "assign" your teachers directly to one of the classes, unlike some other clustering methods would do. Instead LCA estimates for each teacher (i.e. individual in your data set) a probability for belonging to a class. I assume that your dataset there were 4 teachers for which class 4 had the highest estimated probability? You can look at these probabilities to see how "certain" the classification is. If these probabilities are very high, you might feel more confident than when these probabilities are close to the probabilities of other classes (say, when all classes have a probability of about 1/4).

Another relevant check would be to check the parameter estimates of the latent class model, in particular the parameters for the class sizes. What are the estimated standard errors and are these reasonable?

You can also consider a resampling approach to check the stability of your model (e.g. by bootstrap or cross-validation).

Finally, you might want to consider reading these two excellent papers that have relevance for your situation:

Nylund, K.L., Asparouhov, T., & Muthén, B. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling. A Monte Carlo simulation study. Structural Equation Modeling, 14, 535-569.

Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.

Hope this helps.

I agree with previous comments. I think that you should look at several information criterion (AIC, BIC, CAIC, etc) because sometimes results may vary. However I think that the small size of a latent class is not an issue, especially if can be interpreted.

Dear Maarten

many thanks for your comment and recommendation. The article by Nylund et al. (2007) is very helpful indeed. Unfortunately, I my university does not provide access to the one by Muthén & Muthén.

May I ask you another question? I have already looked at the class probabilities, i.e. with what certainty those individuals are grouped together. We call it "hitrate", though I do not know if that is an official term. The results are:

1. class (0,93)

2. class (0,90)

3. class (0,95)

4. class (0,91)

You then wrote: " If these probabilities are very high, you might feel more confident than when these probabilities are close to the probabilities of other classes (say, when all classes have a probability of about 1/4)."

They are high, which is good, but:

1. Is it a bad thing when class probabilities are all in the 90s?

2. Where does you "1/4" come from? My cut-off criterion for class probabilities is >0,80.

I would be fantastic if you could help me out again.

----------------------------------------------------

Dear Paolo

I noticed how, depending on certain information criterion, results vary drastically. The article recommended by Maarten elaborates on that. Thanks for backing me up on this.

Many thanks

Marcel

Hi Marcel,

I think we are not talking about the same probabilities. I was referring to what is commonly called the posterior class-membership probabilities. For each individual there is a posterior probability for (belonging to) each of the classes. As there are 4 classes there are 4 probabilities per individual which by definition have to sum to 1. In case that there is much uncertainty about class membership these probabilities will be around 1/4 for each class (= most class-membership uncertainty).

The posterior class-membership probabilities are very different from hit rates, which I find much more difficult to interpret.

Dear Maarten

I figured out where to find the posterior probabilities for the for the four individuals that were grouped together. The first four colums represent the four variables in the LCA, the last column is the group number. With the exception of the one bold individual, the look alright to me. Like I said, nobody has ever mentioned posterior probabilities to me, so I reckon, nobody would ask for them anyway.

Do you think this would additionally justify my 4-group solution?

Many thanks

Marcel

V1 V2 V3 V4 Class

0.929 0.000 0.071 0.000 4.000

1.000 0.000 0.000 0.000 4.000

0.545 0.000 0.455 0.000 4.000

1.000 0.000 0.000 0.000 4.000

Hi Marcel,

Let me elaborate a bit to explain my suggestions.

It is important to know that latent class analysis is based on a parametric model. This is why latent class analysis is sometimes called model-based clustering and is unlike some other clustering methods such as K-means clustering. This property of the latent class analysis has some advantages and disadvantages (e.g. see goo.gl/Cp9UEK).

Because latent class analysis is parametric it makes sense to first evaluate the estimated latent class parameters. These are often forgotten - or at least not reported - but may reveal important information. Each variable you put into the model (manifest variable) is related to the classes via a coefficient, not unlike regular regression. Assuming you have used the “standard” latent class model (which assumes conditional independence, e.g. see goo.gl/aTSvQJ), and depending on the exact parameterization, there will be probably be 3+(4xJ) of these coefficients in your model, where J stands for the number of manifest variables you have put in.

I advised to check whether the estimated (maximum likelihood) standard errors for each of the latent class model parameters are reasonable. This is because very high standard errors for one of the parameters may reveal the (whole) model is not “identifiable”: which means that the estimated latent class model is not unique and that different sets of parameters for the same data set are just as reasonable (i.e. the latent class model solution is not trustworthy and needs modifications, e.g. see goo.gl/ok8Mxt). Notice that these parameters are also important for your situation, because they define for each individual the posterior class-membership probability and as a consequence also the assigned classes that you use in your analyses. Some of the probabilities that you included in your preceding answer are on their natural boundaries (0 or 1) which already provides some clues that the model may not be identified (hence, more reasons to check the parameter standard errors).

Your original question was about the size of the 4th class that supposedly had n=4 individuals assigned to it. For each of these 4 individuals you can check the posterior class-membership probabilities for the 4th class: these probabilities will reveal whether there is certainty that these individuals belong to the fourth class.

In your preceding answer you say you haven’t heard about these probabilities and that “nobody would ask for them anyway”. You might be right that these probabilities are not often shown in publications, but I do feel that they have value. In case your manifest variables are categorical you may provide the probabilities in table form (e.g. see goo.gl/HdkByz) or otherwise there are probably ways to visualize these probabilities.

Again, these are just suggestions and I hope they will be of help to you.

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http://www.statmodel.com/bmuthen/articles/Article_111.pdf