On information in static and dynamic factor models

This paper employs concepts from information theory in factor models. We show that in the exact factor model the whole distribution of eigenvalues of the covariance matrix contributes to the information and not only the largest ones. In addition, we derive the condition that the first q say eigenvalues diverge whereas the rest remain bounded in the static model rather than having to assume it. Finally, we calculate information in static and dynamic factor models, which can be used to find the dimensions of the factor space. We illustrate the concepts with simulation experiments.

Optimal selection of households for direct marketing by joint modeling of the probability and quantity of response

We present several methods for the maximization of expected profits when households are selected from a mailing list for a direct mail campaign. The response elicited from the campaign can vary over households, as is the case with fund raising or mail order selling. The decisions taken by the household are (a) whether to respond and, in the case of response, (b) the quantity of response, e.g. the sum donated or the monetary amount of the order. We jointly model both decisions and derive a number of profit maximizing selection methods. We empirically illustrate the methods using a data set from a charitable foundation. It appears that modeling both aspects of the response yields considerably higher profits relative to selection methods that are based on solely modeling the response probability.

A criterion for the number of factors

This note proposes a new criterion for the determination of the number of factors in an approximate static factor model. The criterion is strongly associated with the scree test and compares the differences between consecutive eigenvalues to a threshold. The size of the threshold is derived from a hyperbola and depends only on the sample size and the number of factors k. Monte Carlo simulations compare its properties with well-established estimators from the literature. Our criterion shows similar results as the standard implementations of these estimators, but is not prone to a lack of robustness against a too large a priori determined maximum number of factors kmax

Testing the proficiency to distinguish locations with elevated plantar pressure within and between professional groups of foot therapists

BACKGROUND: Identification of locations with elevated plantar pressures is important in daily foot care for patients with rheumatoid arthritis, metatarsalgia and diabetes. The purpose of the present study was to evaluate the proficiency of podiatrists, pedorthists and orthotists, to distinguish locations with elevated plantar pressure in patients with metatarsalgia. METHODS: Ten podiatrists, ten pedorthists and ten orthotists working in The Netherlands were asked to identify locations with excessively high plantar pressure in three patients with forefoot complaints. Therapists were instructed to examine the patients according to the methods used in their everyday clinical practice. Regions could be marked through hatching an illustration of a plantar aspect. A pressure sensitive platform was used to quantify the dynamic bare foot plantar pressures and was considered as 'Gold Standard' (GS). A pressure higher than 700 kPa was used as cut-off criterion for categorizing peak pressure into elevated or non-elevated pressure. This was done for both patient's feet and six separate forefoot regions: big toe and metatarsal one to five. Data were analysed by a mixed-model ANOVA and Generalizability Theory. RESULTS: The proportions elevated/non-elevated pressure regions, based on clinical ratings of the therapists, show important discrepancies with the criterion values obtained through quantitative plantar pressure measurement. In general, plantar pressures in the big toe region were underrated and those in the metatarsal regions were overrated. The estimated method agreement on clinical judgement of plantar pressures with the GS was below an acceptable level: i.e. all intraclass correlation coefficient's equal or smaller than .60. The inter-observer agreement for each discipline demonstrated worrisome results: all below .18. The estimated mutual agreements showed that there was virtually no mutual agreement between the professional groups studied. CONCLUSION: Identification of elevated plantar pressure through clinical evaluation is difficult, insufficient and may be potentially harmful. The process of clinical plantar pressure screening has to be re-evaluated. The results of this study point towards the merit of quantitative plantar pressure measurement for clinical practice

Dynamic models with latent variables from a system theoretic perspective: theory and applications

In the paper Jöreskog's general static model with latent variables (LISREL) and extensively used in social sciences will be generalized to a dynamic version which, in structure, is equivalent to a stationary version of a discrete state-space model. Parameter identifiability and estimation aspects will be briefly discussed and several examples of applications are given such as dynamic factor modelling, errors-in-variables, models with missing observations, control models with latent variables, .... The so-called state-space approximation approach of time series modelling will be emphasized