I have used a path analysis without any latent variable. I know that measurement error is a huge issue in mediation models. I also know that parceling is one way to deal with measurement error, but because I have the matrix of covariances and means only as an input file for AMOS, there is no way I can create parcels from items. I want to use the estimated reliabilities and run models that correct for measurement error. I don't know how to do this in AMOS. Could you please explain me how I can incorporate error of measurement into the model with observed variables? Will I change my input file? I would much appreciate if you can explain this step by step. I have outputs for path analysis, in other words I did everything, but without this procedure for correcting measurement error.
1 Answer
IIRC, parcelling is a pragmatic approach to latent variable analysis wherein the construct of a factor score is done by simply taking a sum score. If that's what you understand parcelling to be, it is fully possible to create such a sum score from a matrix of means and covariances. You simply sum the means and multiply by the number of factors to obtain the sum score. It's variance, consequently, is calculated by using the law of total variance (minding the multiplicative constant of $p$ where necessary).
$$\text{var} \left(\sum_{i=1}^n X_i\right) = \sum_{i=1}^n \text{var} (X_i) +\sum_{i=1}^n \sum_{j=1}^n \text{cov} (X_i, X_j)$$
The covariance between the sum score and an indicator can be derived similarly,
$$\text{cov} \left(\sum_{i=1}^n X_i, X_j \right) = \text{var}(X_j) + \text{cov}_{i \ne j}(X_i, X_j)$$
This is a pragmatic and easy way to create the variable you are after under the constraints you mention. It is not really appropriate to use an approach which you believe to be subpar because the software cannot support what you are trying to do (such as using raw data as input to path modeling). You should drop AMOS in favor of M-plus or lavaan which can do this path modeling with raw data input files.
