Main Effective Parameters Research Articles

Assessment of the performance of a distributed code in relation to the ETp estimates

This article is a preliminary report of a research activityfocusing on the effects of the crop potentialevapotranspiration (ETp) generation methods on boththe performance of a distributed catchment model as well ason the magnitude of its main effective parameters. Thereferred effects were assessed on the basis of theindependent Multi-Calibration (MC) of the distributed modelfor which three different ETp scenarios were generatedas follows: (A) FAO-24 standard approach;(B) FAO-24 approach but used with coefficients of the wind function and of the Stefan-Boltzmann equation selected according to local conditions; and (C) FAO-56 standard approach. ETp was estimated as a function of the reference crop evapotranspiration (ETo) by means of the k c-ETo approach. For assessing the performance of theestimation approach, the ETo outputs of the three scenarioswere compared to local ETo constraints derived from a previous research. The outputs of scenario B and scenario C showed a close agreement with the local ETo constraints. Their effect on the performance of the hydrological model alsoseemed to be comparable. The output of scenario A producedhigher estimates than the outputs of the other two scenarios, inthe order of 200 mm per year. The best model performance was obtained by using the estimates of scenario A. The research alsorevealed the weak dependency of the model effective parametersinspected in this preliminary research on the ETpestimating methods.

Logit Models and Related Quasi-Symmetric Log-Linear Models for Comparing Responses to Similar Items in a Survey

Suppose that subjects respond to a battery of questions (items) of a similar nature in a survey, with each item having the same categorical scale. This article discusses models that express logits for the response distributions in terms of subject and item effects. The models, which generalize the Rasch model, have interpretations referring to subject-specific comparisons of the items. Recent literature shows that one can estimate item parameters using estimates of main effect parameters in corresponding quasi-symmetric log-linear models. We discuss this connection, giving primary attention to ordinal-response models using adjacent-category logits and cumulative logits. For the case of two items, we give expressions for models and corresponding parameter estimates that are the basis of simple tests of marginal homogeneity for square ordinal contingency tables.

Numerical solution of likelihood equations for a first-order response surface model for mixture paired comparisons

A simple procedure for numerical solution of the likelihood equations for estimating the regression parameters of a first-order response surface model for the treatment parameters of mixture paired comparison experiments is developed. It is demonstrated that, for defined rotatable designs, those regression parameters are simple functions of the main effect parameters of a corresponding factorial model with no interactions. The maximum likelihood estimators of those main effect parameters, and hence of their corresponding regression parameters, are obtained through using procedures of treatment contrasts, factorial and iterations. A numerical example is given to illustrate applications of the procedures developed in this paper.

Flunarizine Versus Metoprolol in Migraine Prophylaxis: A Double‐Blind, Randomized Parallel Group Study of Efficacy and Tolerability

The prophylactic effect of flunarizine and metoprolol was studied in a multi-center randomized, double-blind trial of 149 patients with migraine with or without aura. After a 4-week placebo run-in period, patients were randomly allocated to treatment with flunarizine 10 mg daily or metoprolol 200 mg daily for 16 weeks (parallel group design). Both drugs reduced the number of migraine days per month by 37% (95% confidence interval 21-53%) compared with the placebo run-in period. All efficacy parameters were significantly reduced by both drugs and no significant difference was found between the two drugs at any time of the treatment period. However, calculation of the 95% confidence limits showed that each drug may have a superiority of more than 100% on a single main effect parameter. The most common adverse experiences were day-time sedation (both drugs) and weight gain (flunarizine). Depression was the most serious side-effect occurring in 8% on flunarizine and 3% on metoprolol. We conclude that both drugs are effective in the prevention of migraine attacks but a higher number of dropouts occurred on flunarizine because of depression or weight gain.

Sequential unbiased estimation of parameters in a two-way contingency table

Classical analysis of contingency tables employs (i) fixed sample sizes and (ii) the maximum likelihood and weighted least squares approach to parameter estimation. It is well-known, however, that certain important parameters, such as the main effect and interaction parameters, can neverbe estimated unbiasedly when the sample size is fixed a priori We introduce a sequential unbiased estimator for the cell probabilities subject to log linear constraints. As a simple consequence, we show how parameters such as those mentioned above may. be estimated unbiasedly. Our unbiased estimator for the vector of cell probabilities is shown to be consistent in the sense of Wolfowitz (Ann. Math. Statist. (1947) 18). We give a sufficient condition on a multinomial stopping rule for the corresponding sufficient statistic to be complete. When this condition holds, we have a unique minimum variance unbiased estimator for the cell probabilities.

Improved likelihood ratio tests for complete contingency tables

SUMMARY Lawley (1956) describes how asymptotic likelihood ratio tests can in general be improved by multiplying the -2 log A test statistic by a multiplier chosen so that the null distribution of the modified statistic is better approximated by its asymptotic x2 distribution. This paper applies this technique to asymptotic likelihood ratio tests of hypotheses concerning complete contingency tables. Improved tests are derived for hypotheses with closed form maximum likelihood estimators. An asymptotic likelihood ratio test of a composite null hypothesis against a composite alternative can in general be obtained by comparing -2 log A with a x2 distribution, where A is the ratio of maximized likelihoods under the two hypotheses. Lawley (1956) showed that such tests can be improved by multiplying -2 log A by a scale factor chosen so that the null distribution of the resulting statistic has the same moments as X2 ignoring quantities of order n-2, where n is the size of the sample. When the statistic - 2 log A can be expressed as an explicit function of the observations the multiplier is most easily found by calculating directly its expectation as far as terms of order n-1. These improved likelihood ratio tests have been most used in the area of multivariate analysis. In recent years considerable progress has been made in developing methods for analyzing multidimensional contingency tables using log linear models. A comprehensive review is given by Plackett (1 974). In these models the cell frequencies may be regarded as independent Poisson variables whose log expectations are linear in a hierarchical set of main effect and interaction parameters. The -2 log A statistic for testing the goodness of fit of a given model takes the form S = 2EX log (X/u), where the X are the cell frequencies and the ,u are the maximum likelihood estimators of their expectations. In practice X log (X/,u) can be replaced by zero when X = 0. Following Nelder & Wedderburn (1972), S will be termed the deviance of the model. To test a given model with deviance S1 against an alternative with additional estimated parameters and deviance S2, the likelihood ratio test statistic iS S1-S2

A Randomized Procedure of Saturated Main Effect Fractional Replicates

Ehrenfeld and Zacks [2] presented randomized procedures for regular fractions and Zacks [3], [4] showed that an unbiased estimator of a given parameter vector in the saturated fractional replicate case exists only if one randomizes over all possible designs of a certain structure. In this paper, a similar method to the Randomized Procedure I in their paper is given for the saturated irregular main effect fractional replicates and an unbiased estimator of the main effect parameter vector is presented. Prior to this presentation, an invariant property of the information matrix is investigated. The explicit expression of the variance of the estimator is a remaining problem.

Models for Complex Contingency Tables and Polychotomous Dosage Response Curves

Probability models, in terms of main effect and interaction parameters, are given for the cell frequencies of complex contingency tables. These models, related to the logistic handling of quantal data, are essentially the same ones ordinarily employed by others who have studied such tables. The identification of specific parameters rather than of parametric conditions is intended to facilitate understanding what has been done in the field and to stimulate further research on contingency tables. Parametrization is given alternatively in arithmetric and logarithmic terms, with arithmetic additivity corresponding to unions of events (categories), logarithmic additivity to intersections. An analogous model is presented for the handling of the polychotomous dosage response situation, one in which drug treatment may elicit any of several discrete responses. Slope and intercept parameters are postulated corresponding to each of the several possible responses. Alternative handlings of the polychotomous response problem are discussed and it is brought out that the proposed model, in contrast, gives a unique result without the need for specifying an ordering of response categories. Further, the need for considering certain correlation problems and certain unrealistic consequences arising in multivariate probit models are avoided. In the polychotomous response situation it is brought out that arbitrary combination of response categories is inappropriate, albeit corresponding combinations are permissible in the complex contingency table situation. The implications of this limitation are discussed. Possible extensions of the model, including multiple regression and non-linear regression forms, are mentioned.