Measurement errors in predictor variables bias multiple regression coefficients, and the problem is particularly complex with nonlinear models containing product variates. This article presents formulas and computing algorithms for correcting data before regression analyses in order to eliminate biases due to measurement errors in models with second- and third-order product variates (e.g., YZ and XYZ). The method requires independent estimates of error variances and covariances for the first-order variates (e.g., X, Y, and Z). An analysis of empirical data illustrates the approach. Errors in estimates are examined through Monte Carlo analyses.
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References
1.
BOHRNSTEDT, G. W.
and A. S. GOLDBERGER (1969) “On the exact covariance of products of random variables.”J. of the Amer. Stat. Assn.64: 1439-1442.
2.
BOHRNSTEDT, G. W.
and G. MARWELL (1978) “The reliability of products of two random variables,” in K. F. Schuessler (ed.) Sociological Methodology. San Francisco: Jossey-Bass.
3.
BUSEMEYER, J. R.
and L. E. JONES (1983) “Analysis of multiplicative combination rules when the causal variables are measured with error.”Psych. Bull.93: 549-562.
4.
FOX, J.
(1984) Linear Statistical Models and Related Methods. New York: John Wiley.
5.
FULLER, W. A.
and M. A. HIDIROGLOU (1978) “Regression estimation after correcting for attenuation.”J. of the Amer. Stat. Assn.73: 99-104.
6.
GOLDBERGER, A. S.
(1964) Econometric Theory. New York: John Wiley.
7.
HEISE, D. R.
(1975) Causal Analysis. New York: John Wiley.
8.
HEISE, D. R.
(1978) Computer-Assisted Analysis of Social Action. Chapel Hill, NC: Institute for Research in Social Science.
9.
HEISE, D. R.
(1979) Understanding Events: Affect and the Construction of Social Action. New York: Cambridge Univ. Press.
10.
HEISE, D. R.
and L. SMITH-LOVIN (1981) “Impressions of goodness, powerfulness, and liveliness from discerned social events.”Social Psychology Q.44: 93-106.
11.
KENDALL, M. G.
and A. STUART (1969) The Advanced Theory of Statistics. Vol. I. London: Charles Griffin.
12.
KENNY, D. A.
and C. M. JUDD (1984) “Estimating the nonlinear and interactive effects of latent variables.”Psych. Bull.96: 201-210.
13.
SMITH-LOVIN, L.
and D. R. HEISE (1982) “A structural equation model of impression formation,” in N. Hirschberg and L. G. Humphreys (eds.) Multivariate Applications in the Social Sciences. Hillsdale, NJ: Lawrence Erlbaum.
14.
TATE, R. L.
(1984) “Limitations of centering for interactive models.”Soc. Methods & Research13: 251-271.
15.
WARREN, R. D.
, J. K. WHITE, and W. A. FULLER (1974) “An errors-in-variables analysis of managerial role performance.”J. of the Amer. Stat. Assn.69: 886-893.
