Q2. What is the gi in a given model?
In a given model, (gi contains components of zgi (observed variables), unobservable variables such as measurement errors, disturbance terms of regression equations, latent factors, etc.
Q3. What is the common approach to moment structure analysis?
A common approach to moment structure analysis is based on minimum distance (MD) methods, in which a structured vector o- = o- (i() of population moments (usually first- and second-order moments) is fitted to the vector s of corresponding sample moments (Hansen, 1982; Chamberlain, 1982; Browne, 1984; Abowd and Card, 1989).
Q4. What are the main uses of mean and covariance structure models?
Mean and covariance structure models are nowadays widely used in social, economic, and behavioral studies to analyze linear relationships among variables, some of which are unobservable (latent) or subject to measurement error.
Q5. What is the validity of the NT approach?
The analysis of this type of model is usually carried out under the assumption that the observable variables are normally distributed; in the present paper, however, the authors are concerned with the validity of the NT approach when the latent regressor xgi and the disturbance terms vgi deviate from the normality assumption.
Q6. What is the normal component of the latent regressor?
When the latent regressor is random, 5goi is the constant unit element and the nonnormal components are vgi and xgi; in both cases, r = (a,/3, au2)', and the normal component (gL i is (ulg,U2g)'.
Q7. What is the issue the authors address in the present paper?
The issue the authors address in the present paper concerns the analysis of the models described previously using MD methods (or equivalent maximum likelihood [ML] methods) that are based on the assumption that the zgi are i.i.d. normally distributed.
Q8. What is the role of the asymptotic variance matrix 1?
The asymptotic variance matrix 1, of \\I7-s, where n is sample size, plays a fundamental role in designing an efficient MD analysis and in assessing the sampling variability of the statistics of interest.
Q9. what is the nt-MD and PML efficiency?
when the distribution of each latent random constituent of the model is symmetric (i.e., A.3 holds), then asymptotic efficiency applies to all the components of the NT-MD and PML estimators.
Q10. What is the effect of the residual vectors on the NT-MD and PML estim?
In addition, the distribution of the residual vector s - S and of the goodness-of-fit test statistic Tv carry over from NT to the general case; in particular, the NT and PML goodness-of-fit test statistics, T and nF, are asymptotically chisquare distributed when the model holds, despite nonnormality.
Q11. what is the asymptotic distribution of the goodness-of-fit test statistic?
-f_(s - &) is asymptotically normal, with zero mean and variance matrix determined by T, V, and F* (i.e., the asymptotic distribution \\/ (s - 5) is free of higher order moments of the zgi); 5. the asymptotic distribution of the goodness-of-fit test statistic Tv of (16) (for any V) is chi square with degrees offreedom given by (14).
Q12. What is the definition of asymptotic robustness?
The validity of inferences based on the normality assumption when the data are not normally distributed has been called asymptotic robustness (Anderson, 1987).
Q13. What is the i.i.d. of the egLgi?
OO ng i=1for suitable mgo X 1 vector /-tOg and mgo X mgo matrix d(O) (b) the {fgei}i, f = l,...,Lg, are independent and identically distributed (i.i.d.)sequences of zero mean and (finite) mge X mgg variance matrices, Ve), with E(6'hi6'e1i) = 0, when h t f (i.e., uncorrelated).(c) the {egLgi}i are i.i.d. normal.
Q14. What is the inverse of the x case?
When the latent regressor is fixed (the so-called fixed x case), the authors assume the limits limn -O n 1~7 Eg The authorX ., g = 1, 2, are finite.