[R] sem-Package BIC calculation wrong!?

[Peter Dalgaard]

> On 30 Mar 2017, at 16:09 , Ludwig Kreuzpointner <Ludwig.Kreuzpointner at psychologie.uni-regensburg.de> wrote:
> 
> To whom it may concern,
> when I was calculating BIC with sem
> e.g. as follows:
> 
> cfa.mod <- cfa(reference.indicators=FALSE, covs=NULL)    
> F1: Sentences, Vocabulary, Sent.Completion, First.Letters, Four.Letter.Words 
> 
> cfa.sem <- sem(cfa.mod, S=Thurstone, N=355) 
> summary(cfa.sem)
> 
> 
> the BIC value is wrong!
> 
> For the example it results 
> 
> BIC =  104.5072
> 
> Correct with a formula I found in text books:
> 
> BIC= χ2 + ln(N)[k(k + 1)/2 - df]
> 
> BIC should be 192.588977895
> 
> 104.5072 I got, when set k=0
> 
> I think there must be a mistake when getting the numbers of parameters.

The generic definition of BIC is -2 log L + p log N, where p is the number of parameters. However, like the log-likelihood itself, it is only determined up to an additive constant, so it is not obvious that one number is more correct than the other.

-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com