Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Nonlinear models and small sample performance of the generalized method of moments

In this paper I explore the issue of nonlinearity (both in the datageneration process and in the functional form that establishes therelationship between the parameters and the data) regarding the poorperformance of the Generalized Method of Moments (GMM) in small samples.To this purpose I build a sequence of models starting with a simple linearmodel and enlarging it progressively until I approximate a standard (nonlinear)neoclassical growth model. I then use simulation techniques to find the smallsample distribution of the GMM estimators in each of the models.

Measurement with Some Theory: a New Approach to Evaluate Business Cycle Models

We propose a method to evaluate cyclical models which does not require knowledge of the DGP and the exact empirical specification of the aggregate decision rules. We derive robust restrictions in a class of models; use some to identify structural shocks and others to evaluate the model or contrast sub-models. The approach has good size and excellent power properties, even in small samples. We show how to examine the validity of a class of models, sort out the relevance of certain frictions, evaluate the importance of an added feature, and indirectly estimate structural parameters.

Multi-sample analysis of moment-structures: Asymptotic validity of inferences based on second-order moments

In moment structure analysis with nonnormal data, asymptotic valid inferences require the computation of a consistent (under general distributional assumptions) estimate of the matrix $\Gamma$ of asymptotic variances of sample second--order moments. Such a consistent estimate involves the fourth--order sample moments of the data. In practice, the use of fourth--order moments leads to computational burden and lack of robustness against small samples. In this paper we show that, under certain assumptions, correct asymptotic inferences can be attained when $\Gamma$ is replaced by a matrix $\Omega$ that involves only the second--order moments of the data. The present paper extends to the context of multi--sample analysis of second--order moment structures, results derived in the context of (simple--sample) covariance structure analysis (Satorra and Bentler, 1990). The results apply to a variety of estimation methods and general type of statistics. An example involving a test of equality of means under covariance restrictions illustrates theoretical aspects of the paper.

Business cycle measurement with some theory

A method to evaluate cyclical models not requiring knowledge of the DGP and the exact specificationof the aggregate decision rules is proposed. We derive robust restrictions in a class of models; use someto identify structural shocks in the data and others to evaluate the class or contrast sub-models. Theapproach has good properties, even in small samples, and when the class of models is misspecified. Themethod is used to sort out the relevance of a certain friction (the presence of rule-of-thumb consumers)in a standard class of models.

Back to square one: Identification issues in DSGE models

We investigate identifiability issues in DSGE models and their consequences for parameter estimation and model evaluation when the objective function measures the distance between estimated and model impulse responses. We show that observational equivalence, partial and weak identification problems are widespread, that they lead to biased estimates, unreliable t-statistics and may induce investigators to select false models. We examine whether different objective functions affect identification and study how small samples interact with parameters and shock identification. We provide diagnostics and tests to detect identification failures and apply them to a state-of-the-art model.

How much structure in empirical models?

This chapter highlights the problems that structural methods and SVAR approaches have when estimating DSGE models and examining their ability to capture important features of the data. We show that structural methods are subject to severe identification problems due, in large part, to the nature of DSGE models. The problems can be patched up in a number of ways but solved only if DSGEs are completely reparametrized or respecified. The potential misspecification of the structural relationships give Bayesian methods an hedge over classical ones in structural estimation. SVAR approaches may face invertibility problems but simple diagnostics can help to detect and remedy these problems. A pragmatic empirical approach ought to use the flexibility of SVARs against potential misspecificationof the structural relationships but must firmly tie SVARs to the class of DSGE models which could have have generated the data.

A scaled difference chi-square test statistic for moment structure analysis

A family of scaling corrections aimed to improve the chi-square approximation of goodness-of-fit test statistics in small samples, large models, and nonnormal data was proposed in Satorra and Bentler (1994). For structural equations models, Satorra-Bentler's (SB) scaling corrections are available in standard computer software. Often, however, the interest is not on the overall fit of a model, but on a test of the restrictions that a null model say ${\cal M}_0$ implies on a less restricted one ${\cal M}_1$. If $T_0$ and $T_1$ denote the goodness-of-fit test statistics associated to ${\cal M}_0$ and ${\cal M}_1$, respectively, then typically the difference $T_d = T_0 - T_1$ is used as a chi-square test statistic with degrees of freedom equal to the difference on the number of independent parameters estimated under the models ${\cal M}_0$ and ${\cal M}_1$. As in the case of the goodness-of-fit test, it is of interest to scale the statistic $T_d$ in order to improve its chi-square approximation in realistic, i.e., nonasymptotic and nonnormal, applications. In a recent paper, Satorra (1999) shows that the difference between two Satorra-Bentler scaled test statistics for overall model fit does not yield the correct SB scaled difference test statistic. Satorra developed an expression that permits scaling the difference test statistic, but his formula has some practical limitations, since it requires heavy computations that are notavailable in standard computer software. The purpose of the present paper is to provide an easy way to compute the scaled difference chi-square statistic from the scaled goodness-of-fit test statistics of models ${\cal M}_0$ and ${\cal M}_1$. A Monte Carlo study is provided to illustrate the performance of the competing statistics.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Spectral analysis of the luteinizing hormone in the blood samples

Generally, medicine books are concentrated almost exclusively in explaining methodology that analyzes fixed measures, measures done in a certain moment, nevertheless the evolution of the measurement and correct interpretation of the missed values are very important and sometimes can give the key information of the results obtained. Thus, the analysis of the temporary series and spectral analysis or analysis of the time series in the dominion of frequencies can be regarded as an appropriate tool for this kind of studies.In this work the frequency of the pulsating secretion of luteinizing hormone LH (thatregulates the fertile life of women) were analyzed in order to determine the existence of the significant frequencies obtained by analysis of Fourier. Detection of the frequencies, with which the pulsating secretion of the LH takes place, is a quite difficult question due topresence of the random errors in measures and samplings, i.e. that pulsating secretions of small amplitude are not detected and disregarded. In physiology it is accepted that cyclical patterns in the secretion of the LH exist and in the results of this research confirm this pattern and determine its frequency presented in the corresponded periodograms to each of studied cycle. The obtained results can be used as key pattern for future sampling frequencies in order to ¿catch¿ the significant picks of the luteinizing hormone and reflect on time forproductivity treatment of women.

Resonant spin tunneling in small antiferromagnetic particles

The paper reports a detailed experimental study on magnetic relaxation of natural horse-spleen ferritin. ac susceptibility measurements performed on three samples of different concentration show that dipole-dipole interactions between uncompensated moments play no significant role. Furthermore, the distribution of relaxation times in these samples has been obtained from a scaling of experimental X" data, obtained at different frequencies. The average uncompensated magnetic moment per protein is compatible with a disordered arrangement of atomic spins throughout the core, rather than with surface disorder. The observed field dependence of the blocking temperature suggests that magnetic relaxation is faster at zero field than at intermediate field values. This is confirmed by the fact that the magnetic viscosity peaks at zero field, too. Using the distribution of relaxation times obtained independently, we show that these results cannot be explained in terms of classical relaxation theory. The most plausible explanation of these results is the existence, near zero field, of resonant magnetic tunneling between magnetic states of opposite orientation, which are thermally populated.

Chemical composition of the small coastal lagoons of the Mediterranean Spanish littoral

About sixty small water bodies (coastal lagoons, marshes, salt pans, channels, springs, etc.) of the Spanish Mediterranean coast were sampled seasonally for one year (1979-1980), in order to study different aspects of their chemical composition. The concentrations of major ions (alkalinity, Cl-, Ca2+, Mg2+, Na+, and K+), nutrients (N.NO-3, N.NO2-, TRP and Si), oxygen and pH were determined for this purpose. The salt concentrations measured range between 0.4 and 361.3 g l-1. The samples have been divided into four classes of salinity (in g l-1): Cl, S < 5; C2, 5 40. Within these classes, the pattern of ionic dominance recorded is remarkably constant and similar to that found in most coastal lagoons (Cl- > So42- > Alk., for the anions, and Na+ > Mg2+ > Ca2+ > K+, for the cations), although other models occur especially in the first class. The dominance of Na+ and Cl-, as well as the molar ratios Mg2+/Ca2+ and Cl- / SO42- ,clearly increase from class Cl to class C4. The hyperhaline waters include different subtypes of the major brine type"c",, of EUGSTER & HARDIE (1978), the Na+ - (Mg2+) - Cl- - (SO42-) being the most frequent. Nutrient concentrations fall within a wide range (N.NO3 from 0.1 to 1100 mg-at 1-1; PRT from 0.01 to 23.56 mg-at l-1 and Si from 1.0 to 502.0 mg-at l-1). The oxygen values are very variable too, ranging between 0 and 14.4 ml l-1. Four different patterns of nutrient distribution have been distinguished based on the mean concentrations of N.NO3-, and TRP (mean values in mg-at l-1): A, N.NO3- < 10, TRP > l ; B, N.NO3- > 100, TRP < 1; C, 10 < N.NO3- < 100, TRP < 1; C, D, N.NO3- < 10, TRP < 1. As a rule, lagoons of low salinity (C1 and C2 classes) display the nutrient pattern C, and lagoons of high salinity (C3 and C4) show the nutrient pattern D. Model A only appears in waters of very low salinity, whereas model B does not seem to be related to salinity.