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This book reconsiders statistical methods from the point of view of
entropy, and introduces entropy-based approaches for data analysis.
Further, it interprets basic statistical methods, such as the
chi-square statistic, t-statistic, F-statistic and the maximum
likelihood estimation in the context of entropy. In terms of
categorical data analysis, the book discusses the entropy
correlation coefficient (ECC) and the entropy coefficient of
determination (ECD) for measuring association and/or predictive
powers in association models, and generalized linear models (GLMs).
Through association and GLM frameworks, it also describes ECC and
ECD in correlation and regression analyses for continuous random
variables. In multivariate statistical analysis, canonical
correlation analysis, T2-statistic, and discriminant analysis are
discussed in terms of entropy. Moreover, the book explores the
efficiency of test procedures in statistical tests of hypotheses
using entropy. Lastly, it presents an entropy-based path analysis
for structural GLMs, which is applied in factor analysis and latent
structure models. Entropy is an important concept for dealing with
the uncertainty of systems of random variables and can be applied
in statistical methodologies. This book motivates readers,
especially young researchers, to address the challenge of new
approaches to statistical data analysis and behavior-metric
studies.
This book provides methods and applications of latent class
analysis, and the following topics are taken up in the focus of
discussion: basic latent structure models in a framework of
generalized linear models, exploratory latent class analysis,
latent class analysis with ordered latent classes, a latent class
model approach for analyzing learning structures, the latent Markov
analysis for longitudinal data, and path analysis with latent class
models. The maximum likelihood estimation procedures for latent
class models are constructed via the expectation-maximization (EM)
algorithm, and along with it, latent profile and latent trait
models are also treated. Entropy-based discussions for latent class
models are given as advanced approaches, for example, comparison of
latent classes in a latent class cluster model, assessing latent
class models, path analysis, and so on. In observing human
behaviors and responses to various stimuli and test items, it is
valid to assume they are dominated by certain factors. This book
plays a significant role in introducing latent structure analysis
to not only young researchers and students studying behavioral
sciences, but also to those investigating other fields of
scientific research.
This book reconsiders statistical methods from the point of view of
entropy, and introduces entropy-based approaches for data analysis.
Further, it interprets basic statistical methods, such as the
chi-square statistic, t-statistic, F-statistic and the maximum
likelihood estimation in the context of entropy. In terms of
categorical data analysis, the book discusses the entropy
correlation coefficient (ECC) and the entropy coefficient of
determination (ECD) for measuring association and/or predictive
powers in association models, and generalized linear models (GLMs).
Through association and GLM frameworks, it also describes ECC and
ECD in correlation and regression analyses for continuous random
variables. In multivariate statistical analysis, canonical
correlation analysis, T2-statistic, and discriminant analysis are
discussed in terms of entropy. Moreover, the book explores the
efficiency of test procedures in statistical tests of hypotheses
using entropy. Lastly, it presents an entropy-based path analysis
for structural GLMs, which is applied in factor analysis and latent
structure models. Entropy is an important concept for dealing with
the uncertainty of systems of random variables and can be applied
in statistical methodologies. This book motivates readers,
especially young researchers, to address the challenge of new
approaches to statistical data analysis and behavior-metric
studies.
This book provides methods and applications of latent class
analysis, and the following topics are taken up in the focus of
discussion: basic latent structure models in a framework of
generalized linear models, exploratory latent class analysis,
latent class analysis with ordered latent classes, a latent class
model approach for analyzing learning structures, the latent Markov
analysis for longitudinal data, and path analysis with latent class
models. The maximum likelihood estimation procedures for latent
class models are constructed via the expectation–maximization
(EM) algorithm, and along with it, latent profile and latent trait
models are also treated. Entropy-based discussions for latent class
models are given as advanced approaches, for example, comparison of
latent classes in a latent class cluster model, assessing latent
class models, path analysis, and so on. In observing human
behaviors and responses to various stimuli and test items, it is
valid to assume they are dominated by certain factors. This book
plays a significant role in introducing latent structure analysis
to not only young researchers and students studying behavioral
sciences, but also to those investigating other fields of
scientific research.Â
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