RQ-week3.Rmd

# Week 3 - Reading questions

```{r include=FALSE}
knitr::opts_chunk$set(warning=FALSE, message=FALSE)
config <- yaml::yaml.load_file("config.yml")
```

#### Reference {-}

[Byrne, Barbara (2005) Factor Analytic Models: Viewing the Structure of an 
Assessment Instrument From Three Perspectives, Journal of Personality 
Assessment 85(1), 17-32](https://www.tandfonline.com/doi/pdf/10.1207/s15327752jpa8501_02)

#### Questions {-}

1. What are the main differences between exploratory factor analysis 
(EFA) and confirmatory factor analysis (CFA)? 
1. In what circumstances should a researcher use EFA and when CFA? 
1. What are the 5 main limitations of EFA, that CFA models overcome? 
1. In what circumstances can a second order CFA be useful? 
1. Compare the four factor analysis techniques we have now discussed: 
PCA (see last week) and the models on page 21 (EFA), page 19/24 
(CFA) and page 26 (second order CFA). Consider the following three 
research situations: which factor analysis technqiue would you prefer 
for each situation and why? 
    a. A researcher has developed a new questionnaire that should 
measure someone’s personality and wants to know how many 
factors there are.
    b. A researcher has used seven items that have been used since 
the 1960 to measure one concept: authoritarianism 
    c. A researcher has recorded someon’s highest completed 
education, the number of years of education someone has taken 
and highest education followed for all respondents in a survey, 
and is unsure which variable to use to measure the concept 
‘education’

```{r echo=FALSE, results = 'asis', eval = config$show_text}
cat("#### Answers {-}

1. p. 17/2 “EFA is primarily a data-driven approach, whereas CFA is 
theoretically grounded” 
1. p. 17/2 “EFA is most appropriately used when links between the 
observed variables and their underlying factors are unknown or 
uncertain (…) One logical application of EFA would be in the 
development of a new assessment measure. (…) In contrast, CFA is 
appropriately used when the researcher has some knowledge of the 
underlying latent variable structure. Based on theory (..) he or she 
postulates relations between the observed measures and the 
underlying factors a priori and then tests this hypothesized structure 
statistically”. 
1. page 18: 
    * in EFA all common factors are either uncorrelated (orthogonal) or 
correlated (oblique). In CFA, this can be specified by the researcher 
    * in EFA all observed variables are influences by all latent variables, in 
CFA, all observed variables are typically only explained by one latent 
variable 
    * in EFA, the unique factors are always uncorrelated when orthogonal 
rotation methods are chosen. In CFA, factors are almost always 
correlated (unless the user puts in an additional constraint) 
    * there is usually no test of model misfit in EFA, in CFA this is always 
the case 
    * in EFA, you cannot test whether factor structure, or loadings are the 
same across groups, whereas in CFA you can 
    * When there are multiple factors (ideally more than two (PL: because of 
model identification)), which can be explained by some common 
theoretical latent construct. 
1. Answers:
    * EFA: there seem to be no clear latent variables, so the structure is 
not clear. I would choose oblique rotation, as [personality is multi-
dimensional, and separate dimensions are likely to be correlated.  
    * CFA or PCA, or EFA could all work. With PCA and EFA one can test 
whether there truly is one factor structure, whereas in CFA, one can 
use model fit statistics to test this. EFA and CFA have the advantage 
that they show how much of the variance is explained.
    * CFA would be the method here. The researcher can use the latent 
variable in any subsequent analysis, and does not have to reply on 
factor scores that partly consist of measurement errors.  
")
```