Showing papers on "Proper linear model published in 1983"
TL;DR: A new linear regression procedure is proposed with no special assumptions regarding the distribution of the samples and the measurement errors and the result does not depend on the assignment of the methods (instruments) to X and Y.
Abstract: Procedures for the statistical evaluation of method comparisons and instrument tests often have a requirement for distributional properties of the experimental data, but this requirement is frequently not met. In our paper we propose a new linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (instruments) to X and Y. After testing a linear relationship between X and Y confidence limits are given for the slope beta and the intercept alpha; they are used to determine whether there is only a chance difference between beta and 1 and between alpha and 0. The mathematical background is amplified separately in an appendix.
1,588 citations
TL;DR: In this article, the problem of specifying and estimating the variance of estimated parameters based on complex sample designs from finite populations is considered and the results are particularly useful when the parameter estimators cannot be defined explicitly as a function of other statistics from the sample.
Abstract: Summary The problem of specifying and estimating the variance of estimated parameters based on complex sample designs from finite populations is considered. The results of this paper are particularly useful when the parameter estimators cannot be defined explicitly as a function of other statistics from the sample. It is shown how these results can be applied to linear regression, logistic regression and log linear contingency table models. An example of the application of the technique to the Canada Health Survey is given.
1,018 citations
TL;DR: The use of sample survey weights in a least square regression analysis is examined with respect to four increasingly general specifications of the population regression model as mentioned in this paper, and the appropriateness of the weighted regression estimate depends on which model is chosen.
Abstract: The rationale for the use of sample survey weights in a least squares regression analysis is examined with respect to four increasingly general specifications of the population regression model. The appropriateness of the weighted regression estimate depends on which model is chosen. A proposal is made to use the difference between the weighted and unweighted estimates as an aid in choosing the appropriate model and hence the appropriate estimator. When applied to an analysis of the familial and environmental determinants of the educational level attained by a sample of young adults, the methods lead to a revision of the initial additive model in which interaction terms between county unemployment and race, as well as between sex and mother's education, are included.
597 citations
TL;DR: In this paper, it is shown how one can construct a model for a jump process depending on an arbitrary intensity measure with the property that if the measure is absolutely continuous it reduces to Cox's regression model for survival data.
Abstract: Summary It is shown how one can construct a model for a jump process depending on an arbitrary intensity measure with the property that if the measure is absolutely continuous it reduces to Cox's regression model for survival data. The model has the property that the maximum likelihood estimator of the parameters are Cox's estimate for the regression parameter and the Nelson-Aalen estimate for the measure. Cox's partial likelihood for the regression parameter becomes a partially maximized likelihood and the model has a property corresponding to S-ancillarity which explains the partial likelihood.
201 citations
TL;DR: The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points and the Sp criterion provides an asymptotically optimal rule for theNumber of variables to enter.
Abstract: The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points. As the number of regressors grows large, the Sp criterion provides an asymptotically optimal rule for the number of variables to enter.
198 citations
TL;DR: The developments in linear regression methodology that have taken place during the 25-year history of Technometrics are summarized in this paper, where the major topics covered are variable selection, biased estimation, robust estimation, and regression diagnostics.
Abstract: The developments in linear regression methodology that have taken place during the 25-year history of Technometrics are summarized. Major topics covered are variable selection, biased estimation, robust estimation, and regression diagnostics.
165 citations
TL;DR: In this article, a method of assessing the influence of specified subsets of the data when the goal is to predict future observations is proposed, assuming a set of observations is available from the general linear model, and assuming prior information about parameters.
Abstract: Assuming a set of observations is available from the general linear model, and assuming prior information about parameters, we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations.
149 citations
01 Oct 1983
TL;DR: In this paper, the authors present methods for quantitatively estimating the significance of a linear regression model, determining approximate confidence regions about estimated regression coefficients, and determining whether one statistical model is significantly better than another.
Abstract: The time series analysis technique of multivariate linear regression is reviewed with special emphasis on application to real time series with only a limited number of sample observations. The finite length records introduce errors in the sample statistics that must be accounted for when examining cause and effect relationships from the linear regression models. Methods are presented for (1) quantitatively estimating the significance of a linear regression model, (2) determining approximate confidence regions about estimated regression coefficients, and (3) determining whether one statistical model is significantly better than another. The expressions quantifying the effects of sampling errors on statistical quantities are equivalent to the expressions used in large-sample-size classical statistics when all of the sample observations are statistically independent. However, this is not generally the case with real geophysical time series, which typically ‘oversample’ inherent low-frequency variability. The developed formalism is based on the effective number of independent observations in the cortex of linear regression models.
126 citations
TL;DR: In this paper, a diagnostic method for assessing the degree to which individual cases and groups of cases influence the Box-Cox likelihood estimate of the transformation parameter for the response variable in linear regression models is described.
Abstract: We describe a diagnostic method for assessing the degree to which individual cases and groups of cases influence the Box-Cox likelihood estimate of the transformation parameter for the response variable in linear regression models. We compare the method to a method proposed by Atkinson (1982) and sketch the extension to explanatory variables. We present two examples.
72 citations
TL;DR: In this article, the covariance matrix of the disturbance vector of the linear regression model is used to test for AR(1) disturbances against MA(2) disturbances, and the test's five percent significance points are tabulated.
TL;DR: In this article, a general formula is derived, which shows that this effect should be better called "regression to the mode", which may depend on the time-spacing of repeated measurements in a stationary population.
Abstract: High measurement values often show on average a spontaneous decrease when remeasured under stationary study conditions This effect is known as “regression to the mean”, a phenomenon widely met in biomedical research In this paper a general formula is derived, which shows that this effect should be better called “regression to the mode” Further it is shown that this effect may depend on the time-spacing of repeated measurements in a stationary population
TL;DR: In this paper, it was shown that the common tests for stability of regression coefficients and of the disturbance variance in linear regression models are independent, which enables the size of the joint test procedure to be controlled exactly.
TL;DR: In this paper, the robust linear predictor is characterized in a general situation by using indicators of sample elements and it is shown that the natural order of the population quantities may be maintained throughout the analysis.
Abstract: Summary This paper shows how a result of Zyskind (1967) on characterization of best linear estimators for general linear models may be applied to generalize and unify the results of the theory of linear prediction in survey sampling. The robust linear predictor is characterized in a general situation. By using indicators of sample elements it is shown that the natural order of the population quantities may be maintained throughout the analysis.
TL;DR: In this paper, a model for mixed continuous and discrete variables is used to explore the bias in the discriminant function (DF) approach to estimation of the coefficients in the multiple-1ogistic regression model.
Abstract: A model for mixed continuous and discrete variables suggested by Chang and Afifi (1974) and Krzanowski (1975) is used to explore the bias in the discriminant function (DF) approach to estimation of the coefficients in the multiple1ogistic regression model. When the data come from this mixed variable model the DF estimator of the coefficients of the continuous variables are asymptotically unbiased. The DF estimator of the intercept and coefficients for the discrete variables may be severely biased. The magnitude of the bias is shown to depend in a systematic way on the true value of the coefficients and the underlying probabilities of the out-come of discrete variables. The implications for analysis are discussed.
TL;DR: The authors constructs sequences of translation and scale invariant adaptive estimators of the regression parameter vector in the linear regression model, and constructs a sequence of translation-and scale-invariant estimators for linear regression models.
Abstract: This paper constructs sequences of translation and scale invariant adaptive estimators of the regression parameter vector in the linear regression model.
TL;DR: In this paper, the problem of testing the intercept following a preliminary test on the regression (vector) is considered, and some nonparametric procedure is formulated and the effect of the preliminary test (on regression) on the size and power of the final test is studied.
Abstract: For the simple regression model in the multivariate case, the problem of testing the intercept (vector) following a preliminary test on the regression (vector) is considered. Some nonparametric procedure is formulated and the effect of the preliminary test (on regression) on the size and power of the final test is studied.
TL;DR: In this paper, several models for the prediction of creep and shrinkage of concrete are compared statistically with test data available in the literature, and the models are algebraically transformed into a linearized form and statistical regression is then carried out.
TL;DR: Linear regression, combined with search over nonlinear parameters, is useful in fitting Sellmeier formulas to dispersion data, and Rational procedures are discussed also for weighting of data sets of unequal precision.
Abstract: Linear regression, combined with search over nonlinear parameters, is useful in fitting Sellmeier formulas to dispersion data. A special advantage accrues in fitting several sets of data to one formula: linear regression permits systematic normalization to a common absolute value. Rational procedures are discussed also for weighting of data sets of unequal precision. The fitting of common formulas to six sets of data on helium, for wavelengths from 0.09 to 2 μm, illustrates the various procedures.
01 Jul 1983
TL;DR: In this article, the authors deal with selection of an optimal subset of variables in a linear regression model based on the criterion of expected residual mean squares, and reject inferior regression models.
Abstract: : This paper deals with selection of an optimal subset of variables in a linear regression model. Based on the criterion of expected residual mean squares, we reject inferior regression models. The derivation of the rule is different from those of the earlier papers in that here we use the simultaneous tests of a family of hypotheses. Using real data, an example is provided to illustrate the application of the proposed procedure. (Author)
TL;DR: In this article, the Lagrangian interpolation representation is used to shift the regression coefficients, an exception being the use of polynomially distributed lag coefficients, which can be used for a wider range of applications.
Abstract: Polynomials are commonly used in linear regression models to capture nonlinearities in explanatory variables. It is less common, however, that polynomials are used to shift the regression coefficients, an exception being the use of polynomially distributed lag coefficients. This note recommends the technique for a wider range of applications and suggests the Lagrangian interpolation representation as the most convenient for practitioners.
TL;DR: In this paper, the authors discuss proposals that are easy to implement, accelerate the implicit enumeration algorithms and aid in the selection of variables in linear regression analysis, and illustrate the effectiveness and usefulness of these proposals with an example.
Abstract: To find the best regression model of p predictor variablesp= l,...k, where k is the number of potential predictor variables, is an important problem. In this paper, we discuss proposals that are easy to implement, accelerate the implicit enumeration algorithms and aid in the selection of variables in linear regression analysis. We illustrate the effectiveness and usefulness of these proposals with an example.
TL;DR: In this paper, it was shown that the assumption of measurement error in the explanatory variables does not always cause regression parameters to be biased towards zero, and the direction of the bias was found to depend on the degree of orthogonality between explanatory variables.
Abstract: In simple linear regression analysis, measurement error in the explanatory variable causes the ordinary least‐squares estimator of the regression parameter to be biased towards zero However, in multiple linear regression, it is shown that the assumption of measurement error in the explanatory variables does not always cause regression parameters to be biased towards zero The direction of the bias is found to depend on the degree of orthogonality between the explanatory variables
TL;DR: In this article, the authors consider the selection of the best subset of independent variables of a fixed size for possible inclusion in a regression model, and show that the classical procedures (largest ρ{R}^2$ to enter) are uniformly invariant Bayes in the sense of Paulson and Kudo.
Abstract: We consider the selection of the best subset of independent variables of a fixed size for possible inclusion in a regression model. The classical procedures (largest $\mathbb{R}^2$ to enter) are shown to be uniformly invariant Bayes in the sense of Paulson (1952) and Kudo (1956).