The data used to evaluate the psychometrics of the mFCCA short version was from the Connect for Health randomized control trial. The trial has previously been described in detail [12, 13]. The one-year trial tested the effectiveness of two clinical-community interventions on improving body mass index (BMI) and quality of life. It enrolled children ages 2–12 years with a BMI > = 85th percentile and was conducted in pediatric primary care practices in Massachusetts. The enhanced primary care arm included clinical decision support tools to alert clinicians to elevated BMIs and guide best practice management, family educational materials, neighborhood resource guides, and a social- and community-informed text messaging program. The health coaching arm received the same enhancements as the other arm in addition to contextually tailored health coaching support. Both arms were found to effectively reduce BMI and improve quality of life [13]. Parents of children in the enhanced primary care arm answered questions relating to their primary care provider, and therefore, only data from that arm were included in the psychometric analysis as it is more typical of primary care. The Mass General Brigham institutional review board approved the trial.

The mFCCA was adapted from the FCCA, and the adaptation process and psychometric analysis have previously been described [10, 11]. Briefly, the mFCCA has 24 items representative of principles of family-centered care and includes questions from eight topical areas (communication, future promotion, decision-making, strength-based, practice structure, family support, care coordination, and cultural competence). Ordinal responses range from 1 to 5, with higher scores indicating a greater perception of family-centeredness, as well as a “not applicable” response.

The length of the scale remained a barrier to uptake for use in research and clinical practice, and therefore, we aimed to shorten it. Three experts in childhood obesity, including a pediatric gastroenterologist and two childhood obesity intervention researchers, reviewed the items and selected nine items. The process was done in consultation with a member of the team who created the original FCCA. She provided guidance on including items with a range of topical areas and item difficulty.

Following the selection of the nine items, we used Rasch modeling to examine the psychometrics of the shortened scale [14, 15] The original version of the FCCA and the mFCCA used item response theory to examine the reliability and validity of the tool [10, 11]. We began by performing an exploratory factor analysis using the principal axis method on the nine items to confirm the unidimensionality of the scale. We determined that any item with a factor loading < 0.4 would be deleted [11]. Using a Scree plot, we reviewed the eigenvalues indicating the number of factors. To measure reliability and the homogeneity of the scale, we calculated the item-total correlations and deleted correlations < 0.3 [16]. We then used a partial credit model to assess the overall fit of the items and calculated item fit statistics to examine how well the data fit the model [17,18,19]. We determined infit and outfit statistics to detect inliers and outliers, and the criteria range was 0.5–1.5 [19, 20]. Standard error and item difficulty were calculated for each item. Item difficulty is represented on a logit scale and ranges from negative, which represents easy items that could easily be incorporated into care, to positive, which represents difficult items that would be more challenging to incorporate into care [14]. We examined potential question bias by performing the Differential Item Functioning (DIF) to understand if an item measures different abilities for subgroups (sex, income, race, and ethnicity). The DIF procedures we used involved an iterative hybrid of logistic regression and item response theory. We used likelihood ratio Chi-square test as the detection criterion with an α level of 0.01, and used McFadden’s pseudo R2 as the magnitude measure. We would expect pseudo R2 measures to be < 0.02 in a no DIF condition based on Cohen’s guideline [20, 21]. To assess the scale’s internal consistency, we calculated a person separation reliability (equivalent to a Cronbach’s alpha) [22]. After conducting the analyses, we reviewed the results to ensure they fell within the predetermined acceptable ranges. All items fell within acceptable ranges; therefore, none were removed based on those criteria. We then removed one additional item (reduced to eight items) to attempt to shorten the scale further and selected an item that would not affect the range of item difficulty. We repeated the analyses, and again, all items fell within acceptable ranges. We repeated this procedure for an additional item (reduced to seven items) and found that the person separation reliability decreased, therefore we opted to keep the scale at eight items to retain its strong psychometric properties. We then calculated a score by averaging responses for the final eight items as was done in the mFCCA. For all analyses, responses that were answered as “not applicable” were set to missing as they were considered to be structurally missing. Mean imputation was used for other missing responses. Participants with > 50% of items missing or “not applicable” were excluded from analyses. R version 3.4.4 and the eRM and lordif packages were used to perform analyses [17, 20, 23].