Bifactor model and infit statistics? Good afternoon, 
I am currently in the process of calibrating an item bank using a GPCM model. So, am I right to assume that the bifactor model allows me to work with my general factor by assimilating it to a one-factor model, without taking into account group factors? That is, I can estimate my item parameters from my factor loadings on the general factor only?
If so, I have some questions about evaluating the fit of my model. The calculation of infit statistics is specific to unidimensional models. Can I compute infit statistics using the general factor or do I have to do this separately for each of the group factors? Or is there a more appropriate method to evaluate the fit of my model when calibration an item bank using a GPCM model?
Thank you in advance.
 A: Good question. As I understand things, you are interested in estimating item parameters for the bifactor scoring model, with the intent of eventually using these parameters to provide scores on the general factor (note the general factor is often also referred to as the primary factor) only. This makes sense because, in almost all applications of the bifactor model I am familiar with, researchers are most interested in the general factor, as opposed to group factors (note group factors may also be referred to as nuance, minor, or specific factors). However, see Caspi et al. (2014) as a notable exception.
So given you are interested in only the general factor, your question is if there is a way to test the fit of only the general factor. The short answer to this is no. Bifactor models have slope parameters corresponding to both the general factor (what you are interested in) as well as the group factor (what you are not interested in). So if you were to assess the fit of the general factor only, you would first need to remove the influence of the group factor from your general factor slopes. There is literature on how to do this (see references below by Ip & Stucky); however, none touch on model fit (your question).
So, in summary, you will need to assess the fit of your entire model, not just parameters that pertain only to the general dimension.
References
Caspi A, Houts RM, Belsky DW, Goldman-Mellor SJ, Harrington H. 2014. The p factor: One general
psychopathology structure in the structure of psychiatric disorders? Clin. Psychol. Sci. 2:119-37.
Ip, E. H. (2010). Empirically indistinguishable multidimensional IRT and locally dependent unidimensional item response models. British Journal of Mathematical and Statistical Psychology, 63(2), 395-416.
Ip, E. H. (2010). Interpretation of the three-parameter testlet response model and information function. Applied Psychological Measurement, 34(7), 467-482.
Stucky, B. D., & Edelen, M. O. (2014). Using hierarchical IRT models to create unidimensional measures from multidimensional data. Handbook of item response theory modeling, 201-224.
Stucky, B. D., Thissen, D., & Orlando Edelen, M. (2013). Using logistic approximations of marginal trace lines to develop short assessments. Applied Psychological Measurement, 37(1), 41-57.
