Models employing single indicators with fixed measurement error variances emphasize theory, and precise theory does not lend itself to brief exposition, but we will try.
In traditional pulse transit time flow meter, inconsistency of ultrasonic transducers leads to measurement error and plane wave theory, bases of transit time flow meter, is valuable only for low-frequency wave propagation in inviscid fluid and will lose feasibility when fluid viscosity is considered.
Researchers should hear saturated factor correlations and entirely free measurement error variances as shouting THEORY IMPRECISION regarding the latent-level causal structure.
Researchers using "lack of certainty" as an excuse to estimate the best indicator's measurement error variance should be heard as theory bashing, theory belittling, or theory deficient – depending on whether their statement is made brutishly, snidely, or as an honest expression of incapacity as theorist.
As such, confirmatory factor analysis focuses analyses on the activation of hypothesized networks as a whole, improves statistical power by modeling measurement error, and provides a theory-based approach to data reduction with a robust statistical basis.
The fixed 1.0 loading scales the latent and the fixed measurement error variance assigns a theory-dictated identity or meaning to the latent.
The fundamental justification is that fixed measurement error variances clarify the modeled theory, and hence improve the investigation and testing of theory.
Measuring test measurement error: A general approach.
His paper, as well his recent PhD thesis (2), shows nicely that being a good statistician who understands sampling surveys and theory of measurement error analysis is necessary but not sufficient in order to make significant contributions to improving mortality surveillance in resource-poor countries.
The chord-based measurement system has been used for a long time in the measurement of track irregularity, however, the error theory is seldom studied.
