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More convincingly, Billiet and McClendon (2000) modelled two substantive concepts (political trust and attitudes towards immigrants), each of which was measured with a polarity-balanced set of items, with a common methods factor loading equally on all items of both concepts. They obtained a solid-fitting model, but only by permitting correlated error between the two positively worded political trust items. To assess whether the methods factor really tapped ARS, they created an observed measure of acquiescence (the sum of the agreements to the political trust and attitude towards immigrants items plus one additional balanced pair of items on another topic).
Because y −y xi − x and z2i = i sy sx z1i = and since n r12 = ∑ ( x i − x )( yi − y ) i =1 n n i =1 i =1 2 2 ∑ ( x i − x ) ∑ ( yi − y ) it follows that r12 = 1 T z1 z2 n or in matrix notation, R= 1 T 1 Z Z = A T FT FA = A T A n n The recognition that the correlation matrix can be reproduced by the product of its transposed factor loadings and the factor loadings is known as the fundamental theorem in factor analysis. indd 36 and R ≈ A Tm* A m* ASSESSING THE QUALITY OF SURVEY DATA 25/01/2012 2:29:28 PM Applying eigenvalue decomposition (also known as canonical decomposition) to the correlation matrix results in R = BLBT where B is the matrix of the eigenvectors and L the diagonal matrix of the eigenvalues, with the eigenvalues in descending order λ1 > λ2 > … > λm* >… > λm.
Converse (1976) classified over 300 items taken from several opinion polls on whether the referent was one on which respondents can be assumed to have direct personal experience or involvement. On such topics she found only trivial differences by educational attainment, while on more abstract issues the more educated were consistently more likely (three to seven percentage points) to provide a substantive response. , 2002). Judd, Krosnick and Milburn (1981) found significantly more measurement error among respondents with low education, suggesting that the task of placing themselves on various political orientation scales was more difficult for them.