Exploratory factor analysis GHQ-12

EGO GHQ-12 EFA 1) Assuming items are continuous Variable: Names are ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11 ghq12 f1 id; Missing are all (-9999) ; usevariables are ghq01 ghq03 ghq05 ghq07 ghq09 ghq11 ghq02 ghq04 ghq06 ghq08 ghq10 ghq12; idvariable = id; Analysis: Type = EFA 1 3 ; 2) Assuming items are categorical Variable: Names are ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11 ghq12 f1 id; Missing are all (-9999) ; usevariables are ghq01 ghq03 ghq05 ghq07 ghq09 ghq11 ghq02 ghq04 ghq06 ghq08 ghq10 ghq12; categorical are ghq01 ghq03 ghq05 ghq07 ghq09 ghq11 ghq02 ghq04 ghq06 ghq08 ghq10 ghq12; idvariable = id; Analysis: Type = EFA 1 3 ;

EGO GHQ-12 EFA 1) Assuming items are continuous EIGENVALUES FOR SAMPLE CORRELATION MATRIX ) Assuming items are categorical EIGENVALUES FOR SAMPLE CORRELATION MATRIX

EGO GHQ-12 EFA 1) Assuming items are continuous PROMAX ROTATED LOADINGS 1 2 ________ ________ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ PROMAX FACTOR CORRELATIONS ) Assuming items are categorical PROMAX ROTATED LOADINGS 1 2 ________ ________ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ PROMAX FACTOR CORRELATIONS

Item residual variances

Correlation -v- regression coefficient Correlation coefficient: The interdependence between pairs of variables i.e. the extent to which values of the variable change together The strength and direction of the linear relationship A fatter ellipse will result in a greater degree of scatter for a regression line of a given gradient, and a lower correlation

Polychoric Correlation - Assumptions A binary or categorical variable is the observed (or manifest) part of an underlying (or latent) continuous variable Here we’ll also assume that latent variables are normally distributed THRESHOLD relates the manifest to the latent variable Uebersax link: http: //ourworld.compuserve.com/homepages/jsuebersax/tetra.htm

Thresholds Figure from Uebersax webpage

2 binary variables. tab sumodd_g sumeven_g | sumeven_g sumodd_g | 0 1 | Total | | | | Total | | 1,119 This is all we see, however ….

… this is what we assume is going on Figure from Uebersax webpage

What we are really interested in is the correlation (r) between the continuous latent variables Computer algorithm used to search for a correlation r and thresholds t 1 and t 2 which best reproduce the cell counts of the 2x2 table

Conclusions EFA can be carried out in Mplus very simply We have demonstrated that it can be dangerous to ignore the ordinal nature of the data when fitting such a model (a practice followed by many!)