Waching daily Oct 1 2017

Hello. In this video I'm going to talk about my work in the area of Latent Class Analysis.

What is Latent Class Analysis?

Often in the social sciences, in the health sciences, for example

a researcher may be investigating a phenomenon

believed to be caused by a variable that can't be measured.

This variable is called latent.

What they can observe are other variables, related to the latent,

but which don't explain the phenomenon directly.

They are called manifest.

Since it is the latent variable that explains the phenomenon,

then it also determines the behavior of the manifest variables.

For example, a project I worked on.

The objective was to assess the lifestyle of female adolescents.

But how can we measure the variable lifestyle? That can't be done!

It's a latent variable.

So we had to use tangible features, such as

time of physical activity, number of steps walked,

number of meals, among others.

Back here, there is a requirement:

all variables, latent and manifest, must be categorical.

In the case of the latent, we can't tell what its categories,

or classes, correspond to, initially.

But it is important for us to define the total number of classes.

This may be, for example, from a previous indication of the literature

or by comparing the results of different possibilities.

This equation is fundamental. It tells us

the probability of a manifest variable vector Y

assuming a value vector y

and the latent variable L

assuming a class c

is equal to the prior probability gamma for latent class c

multiplied by this cumulative product here, which simply means

the product of all rho parameters

associated to the observations present in vector y.

What is each rho? It corresponds to the probability of observing

each category of each manifest variable.

All parameters, gamma and rho,

are tested with countless different values by a computer,

which then determines the configuration most likely to be correct for them.

There is another thing here, the so-called covariates.

The latent class model must have, at least,

the latent and the manifest variables,

but may also have these covariates. Their function, basically,

is to alter the prior probabilities for the latent classes,

through a multinomial logistic regression.

For example, if social class, if age

exert influence over the latent variable, then

you may use them as covariates.

Here it's the inverse of the causal relation

we saw back there with manifest variables.

The covariates determine, or influence, the latent variable.

How can we choose

which manifest variables to use, then?

Opinion-based decisions, which are the most traditional

-- be it the researcher's opinion or someone else's --,

end up having some bias. Because of that,

our research group, based on the literature,

developed an unsupervised algorithm

to select manifest variables.

This algorithm was implemented in the R programming language.

For those who don't know it, there are many tutorials available. Just as an example,

the slides I'm using in this video here were all made in R,

with a minimum of analytic geometry.

About the algorithm: it starts off from all available manifest variables

and tries to decrease the number of those which are actually used,

according to the result they produce

-- only after the results can we assess

the quality of each manifest variable.

That is measured by the Bayesian Information Criterion, the BIC,

which measures the model's ability to explain the observations made,

but penalizing needless complexities,

which are the excess of manifest variables.

The algorithm also tests every number of latent classes

within an adjustable set,

and finally indicates the best number of classes

associated to the best set of manifest variables.

Then it is the researcher's role

to interpret the meaning of each latent class.

That's what we've been doing;

for the future, our intention is to move on to Latent Transition Analysis,

but that's not for this video.