The Use of Marginal Likelihood for a Diagnostic Test for the Goodness of Fit of the Simple Linear Regression Model

Yanagimoto, Takemi; Yanagimoto, Masakatsu

doi:10.1080/00401706.1987.10488187

Cited by 17 publications

(8 citation statements)

References 19 publications

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“…The purpose of the analysis is to confirm whether or not the log reflectance value changes linearly with the mixture rate. Both [2] and [13] have analyzed this data set with their respective methods and consistently found the convincing evidence of nonlinearity between the two variables. In our analysis, we used Epanechnikov kernel and Gaussian kernel respectively.…”

Section: An Examplementioning

confidence: 83%

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A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Mei

Wang

2003

Acta Mathematicae Applicatae Sinica, English Series, English Se

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Recently, Gijbels and Rousson [6] suggested a new approach, called nonparametric least-squares test, to check polynomial regression relationships. Although this test procedure is not only simple but also powerful in most cases, there are several other parameters to be chosen in addition to the kernel and bandwidth. As shown in their paper, choice of these parameters is crucial but sometimes intractable. We propose in this paper a new statistic which is based on sample variance of the locally estimated pth derivative of the regression function at each design point. The resulting test is still simple but includes no extra parameters to be determined besides the kernel and bandwidth that are necessary for nonparametric smoothing techniques. Comparison by simulations demonstrates that our test performs as well as or even better than Gijbels and Rousson's approach.Furthermore, a real-life data set is analyzed by our method and the results obtained are satisfactory.

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Section: An Examplementioning

confidence: 83%

“…A real-life data set from [13] is analyzed by our test in this section. This data set consists of 21 observations of the log reflectance value of a mixture of two types of flour and the mixture rate which varies from 0 to 1 by an increment 0.05.…”

Section: An Examplementioning

confidence: 99%

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Mei

Wang

2003

Acta Mathematicae Applicatae Sinica, English Series, English Se

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“…The LRT statistic for H 0 : b = 0 was constructed by comparing the log-likelihood of the null NB regression model in Equation (16) with that of the misspecified NB regression model in Equation (18) as follows:…”

Section: Simulationmentioning

confidence: 99%

“…Additionally, other non-parametric regression techniques have been used to test lack of fit of parametric regression models; see, e.g. [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Testing the linearity of negative binomial regression models

2013

Journal of Statistical Computation and Simulation

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The negative binomial (NB) is frequently used to model overdispersed Poisson count data. To study the effect of a continuous covariate of interest in an NB model, a flexible procedure is used to model the covariate effect by fixed-knot cubic basis-splines or B-splines with a second-order difference penalty on the adjacent B-spline coefficients to avoid undersmoothing. A penalized likelihood is used to estimate parameters of the model. A penalized likelihood ratio test statistic is constructed for the null hypothesis of the linearity of the continuous covariate effect. When the number of knots is fixed, its limiting null distribution is the distribution of a linear combination of independent chi-squared random variables, each with one degree of freedom. The smoothing parameter value is determined by setting a specified value equal to the asymptotic expectation of the test statistic under the null hypothesis. The power performance of the proposed test is studied with simulation experiments.

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“…Fig. 6(b) displays a plot of residuals against fitted values from a linear regression model on data reported by Yanagimoto and Yanagimoto (1987). These data are of high precision, and interest centres on whether a linear regression model is appropriate.…”

Section: Reference Band For Residual Plotsmentioning

confidence: 99%

Graphical Comparison of Nonparametric Curves

Bowman¹,

Young²

1996

Applied Statistics

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SUMMARY Nonparametric curves occur in a wide variety of contexts, including repeated measurements mean profiles, survivor functions and in different types of smoothing techniques such as nonparametric regression and density estimation. In some cases confidence bands can be attached to these curves as an indication of the variability of estimation. This is more difficult in the case of nonparametric regression and density estimation where bias is present. In the important case of the comparison of two curves, attention can be focused instead on whether there are differences between the curves. In this paper, the idea of a reference band for the comparison of two curves is introduced. The band is derived from the standard error of the difference between the two curves at each point. The bands have a simple hypothesis testing interpretation which applies equally well to smoothing methods where bias occurs. It does not remove the need for a global test of effects of interest, but it can be very useful as a graphical means of exploring where any identified differences might lie, or of explaining why apparent differences do not actually contribute strong evidence of statistical significance to the global comparison of curves. Reference bands for equality are derived and explored in a variety of settings. Reference bands for parallelism are also derived for nonparametric regression models. Reference bands for parametric models, against which nonparametric regression and density estimates can be compared, are derived for linearity and for normality.

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The Use of Marginal Likelihood for a Diagnostic Test for the Goodness of Fit of the Simple Linear Regression Model

Cited by 17 publications

References 19 publications

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

A Note on the Nonparametric Least-squares Test for Checking a Polynomial Relationship

Testing the linearity of negative binomial regression models

Graphical Comparison of Nonparametric Curves

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