# bi-factor cfa, multiple method factors, DWLS vs MLS in lavaan

I'm new to conducting CFA, and would be appreciative of any feedback users could provide. I've seen a few questions on here in the past that are similar but not quite the same to what I'll pose. I'm trying to implement an approach used in a paper by Biderman, Nguyen, Cunningham & Ghorbani (2011) where they examined the structure of the big five personality traits. In sum, they created a CFA model with 3 method bias factors (1 for all items, 1 for positive items, and 1 for negative items) in addition to the 5 personality factors. I'd like to attempt something similar with my data. Below is what I have so far where g is the general factor, method is the negative bias factor, method_p is the positive bias factor, and f1, f2, f3 are the three group factors.

Overall, I have a few questions. (1) Broadly, does how I've structured things below seems reasonable given my aim to model the 3 group and 3 method bias factors? (2) I've fixed the variances to 1 and made the factors orthogonal. Is doing so any different than adding orthogonal = "FALSE" to the CFA function? Finally, I'm using MLS as an estimator per Rhemtualla, Brosseau-Liard & Savalei (2012) as the scale items contain five categories; however, I've seen a lot of recent papers using DWLS when any sort of ordinal indicators are used...has any sort of consensus been reached with respect to what estimator should be used for ordinal data?

m1<- ' g =~Item3+ Item1+Item6+Item9+Item11+Item12+Item14+Item2+Item4+Item5+Item7+Item8+Item10+Item13+Item15+Item16+Item17+Item18+Item19+Item20
f1  =~ Item1 + Item4 + Item5 + Item9 + Item14 + Item18 + Item19
f2 =~ Item2 + Item8 + Item10 + Item13 + Item15 + Item17 + Item20
f3   =~ Item3 +Item6+ Item7 + Item11+ Item12 + Item16
method =~ Item2+Item4+Item5+Item7+Item8+Item10+Item13+Item15+Item16+Item17+Item18+Item19+Item20
method_p =~ Item3+ Item1+Item6+Item9+Item11+Item12+Item14

f1 ~~ 0*f2
f1 ~~ 0*f3
f1 ~~ 0*g
f1 ~~ 0*method
f1 ~~ 0*method_p
f2 ~~ 0*f3
f2 ~~ 0*method
f2 ~~ 0*method_p
f2 ~~ 0*g
f3 ~~ 0*method_p
f3 ~~ 0*method
f3 ~~ 0*g
method ~~ 0*g
method ~~ 0*method_p
method_p ~~ 0*g

f1 ~~ 1*f1
f2 ~~ 1*f2
method ~~ 1*method
method_p ~~ 1*method_p
g ~~ 1*g
f3 ~~ 1*f3'

fit1<- cfa(m1, data=cfa_complete[,2:21],std.lv=TRUE, estimator = "MLS")

• What's your sample size? Jun 5, 2017 at 16:30
• Hello @JeremyMiles, n=950