Term | Explanation |

Measurement model | Model that relates a set of latent (unmeasurable) factors to a larger number of observed variables (indicators) being used to measure them. |

EFA | A technique used to identify the factors, and hence the possible measurement model(s), underlying a large number of observed variables. |

Principle axis factoring | A method of identifying the relationship between these factors and the observed variables from the observed correlations between the variables. |

Kaisers (eigenvalue >1) criterion | A method for deciding how many factors underlie the observed variables, based on extracting only factors that explain more variability than any single observed variable would. |

Cattell's screen plot | A method for deciding how many factors underlie the observed variables, based on using a plot to identify at which point subsequent extracted factors explain only spurious extra variability, and hence should not be retained. |

(Oblique) factor rotation | Factor rotation aids interpretation of factors via rearranging the variance explained between them. A oblique rotation specifically allows factors to be correlated and is hence considered suitable when the expected underlying concepts are likely to be related. |

CFA | A technique used to test the fit of a hypothesised measurement model to the data, generally by comparing the observed and expected covariance matrices. Unlike EFA that seeks to find one or more possible “best” models, CFA attempts to say how good these best models actually are. |

Model χ^{2} statistic | A statistic for the measure of fit between observed data and that expected given the hypothesised measurement model. A χ^{2} statistic significantly different from zero indicates that the observed and expected models differ significantly. However, as sample size increases, the model χ^{2} is increasingly sensitive; for even in simple models, minor differences between expected and observed data can lead to a significant χ^{2} statistic (hence, the need for other fit indices to reflect model fit—eg, comparative fit indices). |

CFI, and the TLI or NNFI | Fit indices based on comparing the model χ^{2} statistic to that for the null model, with model complexity penalised. Both take values between 0 and 1, with the current consensus being that values >0.9 indicate an adequate fit and values >0.95 indicate a good fit. |

RMSEA | A fit index based on adjusting the χ^{2} statistic for the sample size. Current consensus is that good models have an RMSEA of ≤0.05, and that models with RMSEA >0.10 have a poor fit to the observed data. |

SRMR | A fit index based on the standardised difference between the observed covariance and predicted covariance matrices, with a value <0.08 considered as indicating a model with good fit to the observed data. |

CFA, confirmatory factor analysis; CFI, comparative fit index; EFA, exploratory factor analysis; NNFI, non-normed fit index; RMSEA, root mean square error of approximation; SRMR, standardized root mean square residual; TLI, Tucker–Lewis Index.