Latent Gold Tutorial

[Socorro Henson]

Wemight also consider measurement errors as influences on the item responses. So, here I've amended that diagram to add in three new latent variables represented by the ellipses that float above the boxes. From each ellipse there is an arrow going to each box. That represents the influence of the measurement error on each item, and there's one measurement error latent variable for each item. So, in total then, there are four latent variables in the system, only one of which we're really interested in. That's our targeted latent variable, which is the satisfaction.

A latent variable model specifies the relationship between the measured variables, whatever they happen to be, and the latent variables. So, the model kind of captures the whole picture. And, in constructing a model, we consider several questions, first of all being, how many latent variables are there going to be. We usually refer to that as the dimensionality problem and we distinguish between unidimensional models where there's only one target latent variable plus maybe some error variables versus multidimensional problems where there's multiple targeted variables. And, we have models appropriate for either situation.

In survey research, another frequent goal is to develop a shortened version of a survey. In general, we like our surveys to be short but it can become difficult to just throw out questions to shorten a survey unless you're confident that the resulting information is good. Basic truism is that the shorter the survey usually, the less reliable the survey. So, a latent variable model can help you shorten your survey while maintaining adequate levels of reliability and that's one of the frequent uses of these models. In fact, a collection of models based on item response theory are often used just for that purpose, taking longer surveys and understanding how to shorten them while maintaining reliability standards.

Another frequent use of the models is to help evaluate the equivalence of surveys that have been translated into different languages or simply surveys that are used in distinct populations. It's not uncommon nowadays to be surveying populations where there are multiple language groups. And, so, you'll need to have different versions of your survey. But after translation, are the items really functioning the same way? You can use these models to help get a handle on that question.

The other class of models are based on item response theory, or IRT, and this is really a family of models, very diverse, depending on the types of items. These attempt to model responses to questionnaire items as a function of one or more latent variables and these are nonlinear models. In the past, the use of these has pretty much been confined to cognitive testing applications, but that's no longer true. In the last decade or two, their uses expanded greatly into noncognitive arenas. And, in particular, health and medical research; these models are used quite a bit now and so they're viable options for survey researchers, especially in the health fields.

A second class of latent variable models assume that the latent variables are not continuous but rather categorical or discrete. So, that, in using these models you're considering the idea that respondents are not arrayed along continuous dimensions but exist in groups. The groups being unknown initially but you might believe that whatever it is you're measuring really defines types of people rather than continuously classified dimensions along which we place people. And, a key issue in any use of these models is going to be how many groups are there, two groups, three groups? How many? The two broad techniques are sets of models for doing this are latent class analysis and latent mixture modeling. And, they're closely related. Both assume this idea that there are groups or types.

Latent class analysis is usually used when the indicators are binary, having two response options, or polytomous, having more than two, but a small number of response options. So, a binary item, an example would be a true/false item, is this true or false. A polytomous item might be five-point Likert scale in which you ask people their strength of agreement with some statement, for example. Latent class models are used for those kinds of indicators.

Latent mixture models are more general. They can be used with discrete or continuous indicators. And, latent mixture modeling is sometimes used even when you don't really consider there to be any latent variable models. It's a very general technique. And, so, latent mixture modeling is exploded in popularity and there's a lot of applications of it. And, we will touch on this again soon.

On the other hand, there are cases where we don't necessarily view things as continuous dimensions; but rather, we think of a categorization of people. So, for example, consumer research often thinks of consumers as being defined within market segments. So, you have different types of consumers. And, you want to identify how many types there are and maybe even classify respondents in one or more types. That would be a classic example of a categorical latent variable. And, once you decide how many categories there are, you can also use the model to classify people with varying degrees of success, depending on how well the model fits and the strength of relationship between the items and these classifications.

So, once you've located the software, then you need to actually use it. And, using it means kind of two aspects. First, you need to specify the model that you think is appropriate for your data. So, if you're using a factor model, that would involve, perhaps, specifying how many factors there are and which variables are related to which factors. And, once you've done that, then you fit the model to the data. This is an important step because we don't just use the model, estimate them, and carry on. We need to make sure that the model fits the data and it may not fit the data. So, there's a step involved in evaluating the fit of the model. If the fit is good then we can use it. If the fit is not so good, then we're going to have to step back and maybe modify the model, or modify our items, or take some other step that will get us to a point where we have a model that fits well and answers the questions that we want to address.

So, the last step might, if your model didn't fit well, might involve revising the model or alternatively possibly changing your items, dropping them or eliminating them from the model or from the survey altogether, depending on what stage you're at in the survey process. So, obviously Steps 3 and 4 require a lot of discussion. We don't have time here to go into all the details of these but I hope that this brief introduction will help you see the utility of these models and maybe spur you to learn a bit more about them.

As far as software for Item Response Theory, traditionally the programs available for doing Item Response Theory modeling have been a bit difficult to use, unless you're a specialist. However, the latest addition to the set of programs available, which I list here, called IRTPRO, is user-friendly. So, it's relatively easy to use and it contains the latest bells and whistles and enhancements needed to do IRT modeling of a variety of data types.

The next two, BILOG-MG and PARSCALE. BILOG is oriented toward binary items, items that could be answered only two responses, or scored that way. PARSCALE is more general and can handle polytomous responses. Both of those programs are a little bit difficult to use without some sophistication about IRT, but they're both solid programs.

The last one listed there is called WINSTEPS. It's a relatively easy program to use but it only uses models based on what's called the Rasch model, which is a very commonly used model, but it is a little limited in scope compared to the other three.

For latent class analysis, probably the most frequently used program that's dedicated to latent class analysis is called Latent GOLD, and I have a website listing here for it. Latent GOLD is an excellent program. It does latent class analysis. You can also do latent class analysis in Mplus, the program I mentioned a minute ago with regard to confirmatory factor analysis. And, so, latent class analysis, there are probably, I don't know, half a dozen programs that will do it. I only mention these two here because these are probably the two most frequently used ones, but there are others out there.

I should mention that there's also a lot of free software available on the web to do all of these models. And, nowadays, the free software that's out there is relatively good quality. So, you can get, although all the other programs I mentioned here cost money, you can get free software that will do most if not all of these techniques. One in particular, the R-statistical package, contains programs for doing factor analysis, IRT, latent class analysis, and other techniques. However, it requires some programming skill to use that package. It is free though. It's a wonderful set of statistical tools. So, you know, there are pros and cons with these free programs but they are available.

And that ends my presentation. I hope I've given you enough information to make you want to learn more about this. There's lots of resources available on the web. If you Google any of the names of these techniques you can come up with lots of papers and tutorials and so forth, or you can find a workshop somewhere and learn more about a particular one of these that might be interesting to you. Good luck. Thank you.

Epidemiological methods for estimating disease prevalence in humans and other animals in the absence of a gold standard diagnostic test are well established. Despite this, reporting apparent prevalence is still standard practice in public health studies and disease control programmes, even though apparent prevalence may differ greatly from the true prevalence of disease. Methods for estimating true prevalence are summarized and reviewed. A computing appendix is also provided which contains a brief guide in how to easily implement some of the methods presented using freely available software.

3a8082e126