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In particular, bias (the expected value of the difference of an estimated parameter and the true underlying value) occurs if an independent variable is correlated with the errors inherent in the underlying process. There are several different possible causes of specification error; some are listed below.
Consider the model ^ = {} =. The Ramsey test then tests whether (), (), …, has any power in explaining y.This is executed by estimating the following linear regression = + ^ + + ^ +,
The Lagrange multiplier (LM) test statistic is the product of the R 2 value and sample size: LM = n R 2 . {\displaystyle {\text{LM}}=nR^{2}.} This follows a chi-squared distribution , with degrees of freedom equal to P − 1, where P is the number of estimated parameters (in the auxiliary regression).
Nonsampling error, which occurs in surveys and censuses alike, is the sum of all other errors, including errors in frame construction, sample selection, data collection, data processing and estimation methods.
The Hausman test can be used to differentiate between fixed effects model and random effects model in panel analysis.In this case, Random effects (RE) is preferred under the null hypothesis due to higher efficiency, while under the alternative Fixed effects (FE) is at least as consistent and thus preferred.
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
Heckman's correction involves a normality assumption, provides a test for sample selection bias and formula for bias corrected model. Suppose that a researcher wants to estimate the determinants of wage offers, but has access to wage observations for only those who work.
Clustered standard errors assume that is block-diagonal according to the clusters in the sample, with unrestricted values in each block but zeros elsewhere. In this case, one can define X c {\displaystyle X_{c}} and Ω c {\displaystyle \Omega _{c}} as the within-block analogues of X {\displaystyle X} and Ω {\displaystyle \Omega } and derive ...