Representation
    A latent variable is usually represented by a circle.

    Measured variables are represented by a box.

Standard Assumptions
    the factor is uncorrelated with the errors of measurement in
          each of the indicators
    the errors of different indicators are uncorrelated with each other

Parameters
    loadings: the effect of latent variable on the measure; if a measure
          loads on only one factor, the standardized loading is the
          measure's correlation with the factor and can be interpreted
          at the square root of the measure's reliability.
    error variance:  the variance in the measure not explained by the latent
          variable; error variance does not imply that the variance is random
          or not meaningful, just that it is unexplained by the latent variable

Restriction to Achieve Indentification
    (Go to a discussion of standardization in structural equation models.)
    standardized models:  the factor variance is set equal to one
          and all the loadings are free to vary
    unstandardized models:  one of the loadings is set to one
          (called the marker variable), the others are free, and
       the factor variance is free

Identification (one-factor, no correlated errors)
    at least three indicators of the factor or two if the two
          loadings are set equal to each other

Problems in Estimation

    Heywood Cases (read more)
    the standardized loading is larger than one and the error variance is
         negative
    solution to the problem
         treat as specification error
         create a non-linear constraint on the loading
         fix the standardized loading to one (usually you have to subtract
             one from the degrees of freedom outputted by computer programs)

    Empirical Underidentification
    (To learn about empirical underidentification.)
    the correlation between all pairs of indicators is not significantly 
          different from zero
    for three indicators, the product of the three correlations is negative
    the marker variable does not correlate with the other indicators

Conversion from the Standardized to the Unstandardized Solution
    (Go to a discussion of standardization in structural equation models.)
    factor variance: multiply the squared loading of the marker
          variable times the variance of the marker
    loading: multiply the loading by standard deviation of the
          variable divided by the standard deviation of the factor
    error variance: the error path squared times the variance of the measure
          
Conversion from the Unstandardized to the Standardized Solution
    (Go to a discussion of standardization in structural equation models.)
    loading: multiply the loading by standard deviation of the factor
          divided by the standard deviation of the variable
    error path: square root of one minus the standardized loading squared