Changes In Units Of Measurement Research Articles

Units of measurement and directional distance functions with optimal endogenous directions in data envelopment analysis

The virtual profit efficiency model is sensitive with respect to units of measurement as is the related directional distance function. It is shown that the model can be made invariant with respect to changes in units of measurement in a similar vein as the directional distance function. The geometric interpretation of changes in units of measurement in input output space is uncovered and shown to be similar to the interpretation of the underlying base model. A weighted virtual profit efficiency model with focus on input contractions and output expansions in selected dimensions is developed, and differences and similarities between the working of the weighted versus the unweighted base model are uncovered. It is demonstrated how to incorporate Assurance Regions and Cone Ratios in the virtual profit efficiency model.

COMPUTATIONAL IMPLICATIONS FOR THE LEAST SQUARES PARAMETERS OF THE SIMPLE LINEAR REGRESSION MODEL UNDER DATA TRANSFORMATION.

The Least squares method of parameter estimation is considered important due to its relative simplicity, optimal properties and wide economic applications. This paper examines the computational implications for the estimates of regression parameters for a simple linear regression model when there are changes in units of measurement, leading to a new set of data which is a scaled form of the original data. Expressions for the Least Squares estimates of the regression parameters are derived as well as their precision for the new data in terms of the original data.

Employment, Unemployment and Real Economic Growth

We have modeled the employment/population ratio in the largest developed countries. Our results show that the evolution of the employment rate since 1970 can be predicted with a high accuracy by a linear dependence on the logarithm of real GDP per capita. All empirical relationships estimated in this study need a structural break somewhere between 1975 and 1995. Such breaks might be caused by revisions to monetary policy (e.g. inflation targeting) or/and changes in measurement units. Statistically, the link between measured and predicted rate of employment is characterized by the coefficient of determination from 0.84 (Australia) to 0.95 (Japan). The model residuals are likely to be associated with measurement errors.

Unemployment and Inflation in Western Europe: Solution by the Boundary Integral Method

Using an analog of the boundary element method in engineering and science, we analyze and model unemployment rate in Austria, Italy, the Netherlands, Sweden, Switzerland, and the United States as a function of inflation and the change in labor force. Originally, the model linking unemployment to inflation and labor force was developed and successfully tested for Austria, Canada, France, Germany, Japan, and the United States. Autoregressive properties of neither of these variables are used to predict their evolution. In this sense, the model is a self-consistent and completely deterministic one without any stochastic component (external shocks) except that associated with measurement errors and changes in measurement units. Nevertheless, the model explains between ~65% and ~95% of the variability in unemployment and inflation. For Italy, the rate of unemployment is predicted at a time horizon of nine (!) years with pseudo out-of-sample root-mean-square forecasting error of 0.55% for the period between 1973 and 2006. One can expect that the unemployment will be growing since 2008 and will reach ~11.4% [±0.6 %] near 2012. After 2012, unemployment in Italy will start to descend.

Comparative Analysis of Age Dynamics of Average Values of Body Dimensions in Children from Birth to 7 years

Mean values of different body dimensions in different age cohorts of children make it possible to learn a lot about their dynamic changes. Their comparative analysis, as is usually practiced, in fact leads to a simple description of changes in measurement units (mm or cm) at the average level of some body dimension during a shorter or longer period of time. To estimate comparative intensity of the growth process of different body dimensions, the authors use the analogue of Mahalanobis distance, the so-called Kullback divergence (1967), which does not demand stability of dispersion or correlation coefficients of dimensions in compared cohorts of children. Most of the dimensions, excluding skinfolds, demonstrate growth dynamics with gradually reducing increments from birth to 7 years. Body length has the highest integrative increment, leg length about 94% of body length, body mass 77%, and trunk and extremities circumferences 56%. Skinfolds have a non-monotonic pattern of accumulated standardized increments with some increase until 1-2 years of age.

Units of Measurement and the Stone Index in Demand System Estimation

AbstractThe Stone index typically used in estimating linear almost ideal demand systems is not invariant to changes in units of measurement, which may seriously affect the approximation properties of the model. A modification to the Stone index, or use of a regular price index instead, are both desirable practices in estimating linear AI models.

Beat the Système

Americans are frequently thought by our neighbors in the global village to have an aversion to changes in units of measurement. After 100 years, we still have not converted to the metric system, while the rest of the world rushes on with this lingua franca of commerce. And so it is in the world of clinical laboratory measurement. While many of the world's clinical laboratories and clinicians use the Systeme International (SI), we in this country are still using measurements. However, expressing units on a molar rather than a weight basis is thought to be more correct. Many journals, including JAMA , request study results to be reported in SI, although some have retreated from the stance of only. For those clinicians who wish quick conversion between SI and conventional units, there's Beat the Systeme. This is a low-priced, simple, no-nonsense conversion program that runs under Microsoft Windows. It

Nonlinear models, rescaling and test invariance

Several asymptotic tests proposed in the literature are shown not to be invariant to changes in measurement units or, more generally, to various transformations that leave both the model and the null hypothesis invariant. The tests involved include the Wald test (and various generalizations of it), a variant of the Lagrange multiplier test, Neyman's C(α) test, Durbin's (1970) procedure, Hausman-type tests and a number of tests suggested by White (1982). For all these procedures, simply changing measurement units in a way that leaves both the form of the model and the null hypothesis invariant can lead to very different answers. We observe, in particular, that various consistent estimators of the information matrix lead to test procedures with different invariance properties. We then establish general sufficient conditions ensuring that Neyman's C(α) test is invariant to transformations that leave invariant the form of the model. In many practical cases where Wald-type tests lack invariance, we find that a modification of the C(α) test is invariant and hardly more costly to compute than Wald tests. This computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test. The method suggested is applied to regression models with Box-Cox transformations on the variables.

On the lack of invariance of some asymptotic tests to rescaling

Fourteen different tests applicable in nonlinear models are shown not to be invariant to irrelevant changes in measurement units of the variables. The tests studied include procedures suggested by Durbin, Sargan-Mehta, Hausman, and White (e.g., the information matrix test).

Invariance, Nonlinear Models, and Asymptotic Tests

The invariance properties of some well known asymptotic tests are studied. Three types of invariance are considered: invariance to the representation of the null hypothesis, invariance to one-to-one transformations of the parameter space (reparameterizations), and invariance to one-to-one transformations of the model variables such as changes in measurement units. Tests that are not invariant include the Wald test and generalized versions of it, a widely used variant of the Lagrange multiplier test, Neyman's C(a) test, and a generalized version of the latter. For all these tests, we show that simply changing measurement units can lead to vastly different answers even when equivalent null hypotheses are tested. This problem is illustrated by considering regression models with Box-Cox transformations on the variables. We observe, in particular, that various consistent estimators of the information matrix lead to test procedures with different invariance properties. General sufficient conditions are then established, under which the generalized C(a) test becomes invariant to reformulations of the null hypothesis and/or to one-to-one transformations of the parameter space as well as to transformations of the variables. In many practical cases where Wald-type tests lack invariance, we find that special formulations of the generalized C(a) test are invariant and hardly more costly to compute than Wald tests. This computational simplicity stands in contrast with other invariant tests such as the likelihood ratio test. We conclude that noninvariant asymptotic tests should be avoided or used with great care. Further, in many situations, the suggested implementation of the generalized C(a) test often yields an attractive substitute to the Wald test (which is not invariant) and to other invariant tests (which are more costly to perform).

Standardized versus Unstandardized Regression Weights

Behavioral scientists appear widely divided about the merits of standardized versus unstandardized regression weights. The present paper has therefore attempted to clarify the issue by illustrating how the two kinds of weights respond to the following circumstances: selection, or sampling variation, on the independent variable; presence of measurement error; changes in units of measurement; scales that are relative to norms rather than absolute; changes in test length; and selection on dependent and mediating variables. Standardized weights are invariant over changes in the units of measurement; unstandardized weights are invariant over selection on the independent variable (but only on the independent variable) and in the presence of dependent variable error. In general, however, the illustrated circumstances affected both kinds of weights, sometimes quite strongly. Therefore, neither kind of weight appears very robust, neither can be recommended unequivocally for comparing groups, and neither provides a panacea for overcoming problems of analyzing behavioral data.

The Effect of Changes in Units of Measurement on Least Squares Regression Lines

The Effect of Changes in Units of Measurement on Least Squares Regression Lines