Pearson’s Goodness of Fit Statistic as a Score Test Statistic∗
نویسندگان
چکیده
For any generalized linear model, the Pearson goodness of fit statistic is the score test statistic for testing the current model against the saturated model. The relationship between the Pearson statistic and the residual deviance is therefore the relationship between the score test and the likelihood ratio test statistics, and this clarifies the role of the Pearson statistic in generalized linear models. The result is extended to cases in which there are multiple reponse observations for the same combination of explanatory variables.
منابع مشابه
A Bayesian 2 test for goodness-of-fit
This article describes an extension of classical χ goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involves evaluating Pearson’s goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptotically distributed as a χ random variable on K − 1 degrees of freedom, independently of the dimensi...
متن کاملEstimate-based goodness-of-fit test for large sparse multinomial distributions
The Pearson’s chi-squared statistic (X2) does not in general follow a chi-square distribution when it is used for goodness-of-fit testing for a multinomial distribution based on sparse contingency table data. We explore properties of Zelterman’s (1987) D2 statistic and compare them with those of X2 and we also compare these two statistics and the statistic (Lr) which is proposed by Maydeu-Oliva...
متن کاملParameter Estimation in Astronomy with Poisson-distributed Data. Ii. the Modified Chi-square-gamma Statistic
I investigate the use of Pearson’s chi-square statistic, the Maximum Likelihood Ratio statistic for Poisson distributions, and the chi-square-gamma statistic (Mighell 1999, ApJ, 518, 380) for the determination of the goodness-of-fit between theoretical models and low-count Poisson-distributed data. I demonstrate that these statistics should not be used to determine the goodness-of-fit with data...
متن کاملGoodness-of-Fit Assessment of Item Response Theory Models
The article provides an overview of goodness-of-fit assessment methods for item response theory (IRT) models. It is now possible to obtain accurate p-values of the overall fit of the model if bivariate information statistics are used. Several alternative approaches are described. As the validity of inferences drawn on the fitted model depends on the magnitude of the misfit, if the model is reje...
متن کاملIncreasing the power: A practical approach to goodness-of-fit test for logistic regression models with continuous predictors
When continuous predictors are present, classical Pearson and deviance goodness-of-fit tests to assess logistic model fit break down. The Hosmer–Lemeshow test can be used in these situations. While simple to perform and widely used, it does not have desirable power in many cases and provides no further information on the source of any detectable lack of fit. Tsiatis proposed a score statistic t...
متن کامل