This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

/pdf/a-new-look-at-the-statistical-model-identification-3i4zmkfrkp.pdf

A new look at the statistical model identification

Setting of the learning problem consistency of learning processes bounds on the rate of convergence of learning processes controlling the generalization ability of learning processes constructing learning algorithms what is important in learning theory?.

The Nature of Statistical Learning Theory

Criteria for evaluating structural equation models with latent variables are defined, critiqued, and illustrated. An overall program for model evaluation is proposed based upon an interpretation of converging and diverging evidence. Model assessment is considered to be a complex process mixing statistical criteria with philosophical, historical, and theoretical elements. Inevitably the process entails some attempt at a reconcilation between so-called objective and subjective norms.

On the evaluation of structural equation models

Summary: The program MODELTEST uses log likelihood scores to establish the model of DNA evolution that best fits the data. Availability: The MODELTEST package, including the source code and some documentation is available at http://bioag.byu.edu/zoology/crandall―lab/modeltest.html. Contact: dp47@email.byu.edu.

/pdf/modeltest-testing-the-model-of-dna-substitution-2dmippvvyz.pdf

MODELTEST: testing the model of DNA substitution.

In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.

Information Theory and an Extension of the Maximum Likelihood Principle

The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.

Factor Analysis and AIC

This is a preliminary report on a newly developed simple and practical procedure of statistical identification of predictors by using autoregressive models. The use of autoregressive representation of a stationary time series (or the innovations approach) in the analysis of time series has recently been attracting attentions of many research workers and it is expected that this time domain approach will give answers to many problems, such as the identification of noisy feedback systems, which could not be solved by the direct application of frequency domain approach [1], [2], [3], [9].

Fitting autoregressive models for prediction

Information theory as an extension of the maximum likelihood principle

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