Calculate several information or model selection criteria (MSC) such as the Akaike information criterion (AIC), the Bayesian information criterion (BIC) or the Hannan-Quinn criterion (HQ).

calculateModelSelectionCriteria(
.object          = NULL,
.ms_criterion    = c("all", "aic", "aicc", "aicu", "bic", "fpe", "gm", "hq",
"hqc", "mallows_cp"),
.by_equation     = TRUE,
.only_structural = TRUE
)

## Arguments

.object

An R object of class cSEMResults resulting from a call to csem().

.ms_criterion

Character string. Either a single character string or a vector of character strings naming the model selection criterion to compute. Defaults to "all".

.by_equation

Should the criteria be computed for each structural model equation separately? Defaults to TRUE.

.only_structural

Should the the log-likelihood be based on the structural model? Ignored if .by_equation == TRUE. Defaults to TRUE.

## Value

If .by_equation == TRUE a named list of model selection criteria.

## Details

By default, all criteria are calculated (.ms_criterion == "all"). To compute only a subset of the criteria a vector of criteria may be given.

If .by_equation == TRUE (the default), the criteria are computed for each structural equation of the model separately, as suggested by Sharma et al. (2019) in the context of PLS. The relevant formula can be found in Table B1 of the appendix of Sharma et al. (2019) .

If .by_equation == FALSE the AIC, the BIC and the HQ for whole model are calculated. All other criteria are currently ignored in this case! The relevant formulae are (see, e.g., (Akaike 1974) , Schwarz (1978) , Hannan and Quinn (1979) ):

$$AIC = - 2*log(L) + 2*k$$ $$BIC = - 2*log(L) + k*ln(n)$$ $$HQ = - 2*log(L) + 2*k*ln(ln(n))$$

where log(L) is the log likelihood function of the multivariate normal distribution of the observable variables, k the (total) number of estimated parameters, and n the sample size.

If .only_structural == TRUE, log(L) is based on the structural model only. The argument is ignored if .by_equation == TRUE.

## References

Akaike H (1974). “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control, 19(6), 716--723.

Hannan EJ, Quinn BG (1979). “The Determination of the order of an autoregression.” Journal of the Royal Statistical Society: Series B (Methodological), 41(2), 190--195.

Schwarz G (1978). “Estimating the Dimension of a Model.” The Annals of Statistics, 6(2), 461--464. doi:10.1214/aos/1176344136 .

Sharma P, Sarstedt M, Shmueli G, Kim KH, Thiele KO (2019). “PLS-Based Model Selection: The Role of Alternative Explanations in Information Systems Research.” Journal of the Association for Information Systems, 20(4).

## See also

assess(), cSEMResults