Hello,
I'm trying to estimate a minimum sample size and I'm reading Kline's book on structural equation modeling, where he references the N:Q ratio:
"In ML estimation, Jackson (2003) suggested that researchers think about minimum sample size in terms of the ratio of cases (N) to the number of model parameters that require statistical estimates (q)"
I have my model set up in AMOS and it shows the parameters for the weights, covariances, and variances. I understand where they come from, but I'm confused about how to use the N:Q rule because Kline says that its the parameters that require statistical estimates. Does this mean the parameters that I am interested in for my prediction (i.e. the weights and/or covariances) ? Or does it mean the parameters that the entire statistical model requires to make an estimate of fit (i.e. weights + covariances + variances)?
Thanks so much in advance!
My understanding is that Q here refers to all freely estimated (as opposed to fixed) parameters in the model, including (but not limited to) estimated intercepts, factor loadings, factor variances, factor covariances, path coefficients, and residual variances. So you would count everything for which you get a parameter estimate and standard error, but not any fixed parameters (such as, for example, factor loadings that are fixed to 1 a priori for model identification).
I would double check about whether to count residual variances, because they are determined by the other parameters in the model.
David L Morgan It is not generally true (in fact, rather rarely) that the residual variances in path, CFA, or SEM models are functions of (determined by) other model parameters. Residual variances are almost always free (independent) model parameters.
As an aside, when parameters (including residual variances) are set equal to other parameters, they count only as one free parameter.
Thing I was thinking about is that once a "fits" loading in a model, that also determines what the residual variance has to be. So it is "free" in the sense that it is not pre-specified, but it is not "estimated" by the model except in a limited sense, and I was always taught to count only the parameters that are actually being estimated.
David L Morgan The error/residual variances are being estimated independently of the factor loadings so they do count as independent model parameters in most cases. They are not usually determined by the factor loadings or other parameters in standard CFA/SEM. The only parameters that do not count as free parameters are ones that are fixed to specific values (e.g., loadings that are fixed to 1) or parameters that are set equal to other free parameters.
What I was taught was tate because the loading and the error variance together account for 100% of the variance in an item, there is essentially only one degree of freedom, which is why you shouldn't count them both.
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