Maximum likelihood estimation of the Latent Class Model through model boundary decomposition

The Expectation-Maximization (EM) algorithm is routinely used for the maximum likelihood estimation in the latent class analysis. However, the EM algorithm comes with no guarantees of reaching the global optimum. We study the geometry of the latent class model in order to understand the behavior of the maximum likelihood estimator. In particular, we characterize the boundary stratification of the binary latent class model with a binary hidden variable. For small models, such as for three binary observed variables, we show that this stratification allows exact computation of the maximum likelihood estimator. In this case we use simulations to study the maximum likelihood estimation attraction basins of the various strata. Our theoretical study is complemented with a careful analysis of the EM fixed point ideal which provides an alternative method of studying the boundary stratification and maximizing the likelihood function. In particular, we compute the minimal primes of this ideal in the case of a binary latent class model with a binary or ternary hidden random variable.

Abnormal magnocellular pathway visual processing in infants at risk for autism

BACKGROUND

A wealth of data has documented impairments in face processing in individuals with autism spectrum disorders (ASD). Recently, the suggestion has been made that these impairments may arise from abnormal development of a subcortical system involved in face processing that originates in the magnocellular pathway of the primate visual system.

METHODS

To test this developmental hypothesis, we obtained visual perceptual data from 6-month-old infants who were at risk for ASD because they had an older sibling diagnosed with the disorder ("high-risk infants"). To measure sensitivity of the magnocellular (M) pathway and, for comparison, of the parvocellular (P) visual pathway, we employed visual stimuli designed to selectively stimulate the two. Sensitivity data from high-risk infants (n = 13) were compared with data from matched control infants (i.e., "low-risk" infants with no family history of ASD, n = 26).

RESULTS

On the P pathway stimulus, high-risk infants exhibited sensitivities that were identical to those of control infants. By contrast, on the M pathway stimulus, high-risk infants exhibited sensitivities nearly twofold greater than those of control infants.

CONCLUSIONS

Given that ASD and its symptoms are known to run in families, these preliminary results suggest that ASD may be associated with abnormal M pathway function early in infancy, which may aid in early diagnosis of the disorder.