[Forum SIS] seminari DISMEQ, 07.04.16 e 14.04.16

[Claudio Giovanni Borroni]

Segnalo due seminari che si terranno
 
Giovedì 07.04.16 alle ore 10.00 e
Giovedì 14.04.16 alle ore 10.00
 
presso il Dipartimento di Statistica e Metodi Quantitativi (DISMEQ),
Università degli Studi di Milano Bicocca,
via Bicocca degli Arcimboldi, 8 Milano
stanza 4026, quarto piano palazzo U7
 
Relatore: Nobuoki Eshima, Department of Biostatistics, Faculty of Medicine,
Oita University, Japan
 
 
***** Giovedì 07.04.16*****
Titolo: Entropy coefficient of determination for generalized linear models
 
Abstract: Measurement of the predictive or explanatory power of generalized
linear models (GLMs) [1] is important for regression analysis as well as a
model selection. GLMs include various useful regression models such as
normal linear regression, logistic regression, and loglinear models, and are
widely applied in practical data analyses. In normal linear regression, the
coefficient of determination plays an important role on the measurement of
predictive power; however regression models for non-normal responses
especially polytomous ones need other measures for assessing the predictive
powers. By using variation functions of response variables, generalized
coefficient of determinations were proposed as proportions of the variation
explained by explanatory variables. Predictive power measures based on the
likelihood function and entropy can be viewed as the above type ones. The
random component of the GLM is an exponential family distribution, and the
covariance between the response variable and a canonical parameter is
described with the Kullback-Leibler information that measures the difference
between the model concerned and the independent (null) model [2]. The
desirable properties of the predictive power measures for GLMs may be (i)
interpretability; (ii) being the multiple correlation coefficient or the
coefficient of determination in normal linear regression models; (iii)
entropy-based property; (iv) applicability to all GLMs; in addition to
these, it may be appropriate for a measure to have the following property:
(v) monotonicity in the complexity of the linear predictor. In this seminar,
the entropy coefficient of determination (ECD) is explained as a predictive
power measure for GLMs [3]. Basic predictive power measures are compared
with respect to desirable properties for assessing the effects of factors in
GLMs. Advantageous properties of ECD in GLMs are discussed and the ECD
approach is applied to a logit model with polytomous response and
explanatory variables.
[1] Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear model,
Journal of the Royal Statistical Society A; 135: 370­384.
[2] Eshima, N and Tabata, M (2010) Entropy coefficient of determination for
generalized linear models, Computational Statistics and Data Analysis; 54:
1381--89.
[3] Eshima, N. & Tabata, M. (2007). Entropy correlation coefficient for
measuring predictive power of generalized linear models, Statistics and
Probability Letters; 77, 588­593.
 
 
 
***** Giovedì 14.04.16*****
Titolo: An entropy-based approach to path analysis of structural generalized
linear models
 
Abstract: Path analysis is often applied to causal systems of continuous
variables through the linear structural equations model (LISREL) ([1]). In
the approach, causal relationships among variables are described by a path
diagram and translated into linear equations of the variables. Causal
effects can then be calculated by regression and correlation coefficients
obtained for the linear equations. In contrast, path analysis of categorical
variables is more complex than that of continuous variables because the
causal system under consideration cannot be described by linear regression
equations. Kuha and Goldthorpe ([2]) gives a path analysis method for
generalized linear models (GLMs) that uses log odds ratios. In their
approach, first the total, direct and indirect effects are defined on the
basis of log odds ratios. However, additive decomposition of the total
effect into the direct and indirect effects only approximately reflects
reality, and assessing effects in categorical (polytomous) variable systems
become more complicated as the numbers of variable categories are increased.
There is need for a method of path analysis with categorical responses. When
describing causal systems of the variables by GLMs, regression coefficients
are related to log odds ratios, and so it is natural to consider the effects
of explanatory variables according to odds or log odds ratios. In this
seminar, first a practical example of causal systems, British mobility data
[2], is considered to re-analyzes them by a new method of path analysis.
Second, the relation between the log odds ratio and entropy is briefly
reviewed. Third, a path analysis method for causal systems described by GLMs
is introduced [3]. A further application of the path analysis is also given
[4].
[1] Bentler, P.M. & Weeks, D.B. (1980). Linear structural equations with
latent variables, Psychometrika; 45: 289--308.
[2] Kuha, J. & Goldthorpe, J. H. (2010). Path analysis for discrete
variables: The role of education in social mobility, J. R. Statist. Soc. A;
173: 1--19.
[3] Eshima, N, Tabata, M, Borroni, CG and Kano, Y (2015). An entropy-based
approach to path analysis of structural generalized linear models: a basic
idea, Entropy; 17: 5117--5132.
[4] Eshima, N, Borroni, CG and Tabata, M. (2016). Relative importance
assessment of explanatory variables in generalized linear models: an
entropy-based path analysis approach (submitted).
  
 
Tutti gli interessati sono invitati a partecipare.
 
Cordiali saluti, Claudio Borroni


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