Some caveats when using the IHS transformation

Electronic Journal of Statistics, 2013

Ordinary Least Squares (OLS) is recognised as being useful in the context of multiple linear regression but can also be effective under the more general framework of the single-index model. In cases where it is ineffective, transformations to the response can improve performance while still allowing for interpretation on the original scale. In this paper we introduce an influence diagnostic for OLS that can be used to assess its effectiveness in the general setting and which can also be used following response transformations. These findings are further emphasized and verified via some simulation studies.

Computational Statistics & Data Analysis

There exist a number of tests for assessing the nonparametric heteroscedastic location-scale assumption. Here we consider a goodness-of-fit test for the more general hypothesis of the validity of this model under a parametric functional transformation on the response variable. Specifically we consider testing for independence between the regressors and the errors in a model where the transformed response is just a location/scale shift of the error. Our criteria use the familiar factorization property of the joint characteristic function of the covariates under independence. The difficulty is that the errors are unobserved and hence one needs to employ properly estimated residuals in their place. We study the limit distribution of the test statistics under the null hypothesis as well as under alternatives, and also suggest a resampling procedure in order to approximate the critical values of the tests. This resampling is subsequently employed in a series of Monte Carlo experiments that illustrate the finite-sample properties of the new test. We also investigate the performance of related test statistics for normality and symmetry of errors, and apply our methods on real data sets.

2000

ABSTRACT. Variables maybe used as productsi na regressi on modelt ocorrect or adjust for the effects of other variables. Such variables maybe transformed tobecom,ei ndices;for example, tobe constrained tobe between 0 and 1. Weprovi de a theoretical and a practical demonstration thatt he choice of transformation can affect the statistical significance of tests associated with estimates of effects and coefficients

We often transform our data before making a statistical analysis -and a conclusion about some prices is then given in square root of dollar instead of just dollar. What does this mean? In situations where the assumptions for performing inference and estimations are violated transformations are used in order to obtain variables which satisfies the assumptions. Especially, the application of the general Box-Cox transformation is popular. Simulation is another important field where transformations are used. Random variables are transformed in order to obtain new random variables with distributions which approximately are identical to specified distributions. In this paper the theoretical background for transformations is described briefly and examples of various types of transformations are considered. The problems of explaining the results from inference and estimation obtained in the space of transformed variables in the space of the original variables are outlined. Especially, the problems concerning ANOVA and regression analysis are discussed. Simulation examples are given to illustrate the problems for some of the special cases of the Box-Cox transformation.

2015

Accurate estimation of marginal effects is of considerable interest to economists. We use “small disturbance ” asymptotics to obtain analytic expressions for the biases of marginal effect estimators in regression models with a logarithmically transformed dependent variable, and regressors which may be in the levels or logarithms of the variables. Some numerical evaluations suggest that the relative magnitudes of these biases are small, but not as small as their counterparts for elasticity estimators.

Journal of Health Economics, 2000

Economists often estimate models with a log-transformed dependent variable. The results from the log-transformed model are often retransformed back to the unlogged scale. Other studies have shown how to obtain consistent estimates on the original scale but have not provided variance equations for those estimates. In this paper, we derive the variance for three estimates -the conditional mean of y, the slope of y, and the average slope of y -on the retransformed scale. We then illustrate our proposed procedures with skewed health expenditure data from a sample of Medicaid eligible patients with severe mental illness. q

Statistics & Probability Letters, 2004

The functional form used in regression may be generalized by the Box-Cox transformation. We adopt the generalized information criterion (GIC) approach to determine a need for Box-Cox (J. Roy. Statist. Soc. Ser. B 26 (1964) 211) transformation of the response variable. The utilization of the constructed variable reduces the problem to one of variable selection based on GIC. Our method leads to comparing the partial correlation coe cient between the dependent variable and the constructed variable of an artiÿcial regression, with critical values depending on a penalty parameter. The method is illustrated with simulation examples and several well-known examples from the literature in regression diagnostics.

1990

New York Science Journal , 2017

Embarking on various transformations of linear regression model was investigated with a keen interest on the core difference between transformed and untransformed variables whose interdependence is closely related. Mean square error and error diagnostic analysis were adopted as basis for adjudging the best linear regression model. It was deduced from available results that transformations of logarithm (bases 10 and 7), square root, reciprocal and inverse square were found to have among others possessed the minimum mean square errors of 0.001 and lesser. In contrary, when compared with the qq-plots and other residual plots from the diagnostic analysis, logarithm transformation of base 10 was acknowledged to have performed better among other transformation competitors. Therefore, error diagnostic analysis should form part of reliable yardsticks apart from the minimum condition of least mean square error for selecting best linear regression model when transformations of closely related variables with same number of observations are involved.