extending the Akaike Information Criterion to mixture regression models

We examine the problem of jointly selecting the number of components and variables in finite mixture regression models. We find that the Akaike Information Criterion is unsatisfactory for this purpose because it overestimates the number of components, which in turn results in incorrect variables being retained in the model. Therefore, we derive a new Information Criterion, the mixture regression Criterion (MRC), that yields marked improvement in model selection due to what we call the “clustering penalty function.” Moreover, we prove the asymptotic efficiency of the MRC. We show that it performs well in Monte Carlo studies for the same or different covariates across components with equal or unequal sample sizes. We also present an empirical example on sales territory management to illustrate the application and efficacy of the MRC. Finally, we generalize the MRC to mixture quasi-likelihood and mixture autoregressive models, thus extending its applicability to non-Gaussian models, discrete responses, and d…

semiparametric and additive model selection using an improved Akaike Information Criterion

Abstract An improved AIC-based Criterion is derived for model selection in general smoothing-based modeling, including semiparametric models and additive models. Examples are provided of applications to goodness-of-fit, smoothing parameter and variable selection in an additive model and semiparametric models, and variable selection in a model with a nonlinear function of linear terms.

smoothing parameter selection in nonparametric regression using an improved Akaike Information Criterion

Summary. Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a Criterion based on the Akaike Information Criterion (AIC), termed AICc, is derived and examined as a way to choose the smoothing parameter. Unlike plug-in methods, AICc can be used to choose smoothing parameters for any linear smoother, including local quadratic and smoothing spline estimators. The use of AICc avoids the large variability and tendency to undersmooth (compared with the actual minimizer of average squared error) seen when other ‘classical’ approaches (such as generalized cross-validation or the AIC) are used to choose the smoothing parameter. Monte Carlo simulations demonstrate that the AICc-based smoothing parameter is competitive with a plug-in method (assuming that one exists) when the plug-in method works well but also performs well when the plug-in approach fails or is unavailable.

recursive segmentation procedure based on the Akaike Information Criterion test

This study proposes a recursive segmentation procedure for multivariate time series based on Akaike Information Criterion. The Akaike Information Criterion, between independently identically distributed multivariate Gaussian samples and two successive segments drawn from different multivariate Gaussian distributions, is used as a discriminator to segment multivariate time series. The bootstrap method is employed in order to evaluate the statistical significance level. The proposed method is performed for an artificial multi-dimensional time series consisting of two segments with different statistics. The log-return time series of currency exchange rates for 30 currency pairs for the period from January 4, 2001 to December 30, 2011 are also divided into 11 segments with the proposed method. This method confirms that some segments correspond to historical events recorded as critical situations.

COMPSAC – Recursive Segmentation Procedure Based on the Akaike Information Criterion Test

This study proposes a recursive segmentation procedure for multivariate time series based on Akaike Information Criterion. The Akaike Information Criterion, between independently identically distributed multivariate Gaussian samples and two successive segments drawn from different multivariate Gaussian distributions, is used as a discriminator to segment multivariate time series. The bootstrap method is employed in order to evaluate the statistical significance level. The proposed method is performed for an artificial multi-dimensional time series consisting of two segments with different statistics. The log-return time series of currency exchange rates for 30 currency pairs for the period from January 4, 2001 to December 30, 2011 are also divided into 11 segments with the proposed method. This method confirms that some segments correspond to historical events recorded as critical situations.

comparing time activity curves using the Akaike Information Criterion

The comparison of curves is a common task in many fields of science. Simply comparing the sums of squares or R2 is not sufficient, and frequently used tests have many disadvantages. The basic idea of the presented method is turning the problem of comparing curves into a problem of model selection using the corrected Akaike Information Criterion. Here, this straightforward approach is applied for comparing curves using the example of 111In- and 90Y-labelled anti-CD66 antibody serum time activity data. As a result it is shown that for the investigated 111In- and 90Y-labelled anti-CD66 antibodies, the biokinetics between dosimetry and therapy are different with respect to the contribution of the second, longer half-life component. We advocate the use of the presented method rather than employing less advanced approaches for curve comparison.

model selection for time activity curves the corrected Akaike Information Criterion and the f test

Data analysis often requires a multi model approach, i.e. the best model or models are selected from a well chosen set of candidate models and subsequent parameter inference is conducted. The selection of the model or models which are best supported by the data can be accomplished using various criteria. The present work focuses on the comparison of two approaches namely the corrected Akaike Information Criterion (AICc) and the F-test for sparse data sets, which are common in medical research. The selection of the true model and the determination of relevant pharmacokinetic parameters as the clearance, the volume of distribution and the mean residence time are examined using Monte Carlo simulations with 10000 replications. The data (N=10 per replication) are generated from a sum of two exponentials, which parameters were determined by fitting to time-concentration data of 111In labelled anti-CD66 antibody in blood serum. Four different normal distributed multiplicative statistical errors (0.05, 0.1, 0.15, 0.2) were examined.

The set of candidate models consists of sums of up to 3 exponentials. Comparisons with two different model set sizes were conducted. All candidate models are fitted to the generated data and selected according to the AICc and the F-test.

Both selection criteria perform well for our data. The selection frequency of functions of lower dimension increases proportionally to the statistical error for both criteria, while for higher errors, the AICc tends to choose a model of lower dimension more frequently than the F-test. In addition, the overfitted fraction decreases proportionally to the statistical error for both methods but selection frequency of function of higher dimension is larger using the F-test.

The choice of the adequate model set is important for the positive effect of model averaging concerning the bias and the variability of the estimated parameters. It is in general assumed and has been confirmed in this study that parameter estimation using the AICc has clear advantages over the F-test.

choosing the optimal fit function comparison of the Akaike Information Criterion and the f test

In many circumstances of data fitting one has to choose the optimal fitting function or model among several alternatives. Criteria or tests on which this decision is based are necessary and have to be well selected. In this preliminary analysis the application of the corrected Akaike Information Criterion is demonstrated considering the example of determining pharmacokinetic parameters for the blood serum time activity curves of {sup 111}In-labeled anti-CD66 antibody. Another model selection Criterion, the F-test, is used for comparison. For the investigated data the corrected Akaike Information Criterion has proved to be an effective and efficient approach, applicable to nested and non-nested models.