Statistical analyses
ACEs
MINOR
Descriptive statistics for a wide range of descriptors were selected to characterize the sample by treatment group. Longitudinal outcomes were analyzed using linear mixed analysis of repeated measures models for continuous outcomes and generalized estimating equations for count outcomes (Poisson distribution for CIS-Physical Integration and negative binomial distribution for GAIN-SS and ED Visits), assuming an unstructured correlation matrix for the repeated measures. Percentage of days stably housed over the 24-months follow-up (range 0–100%) was modeled as a continuous outcome in a linear model. We also performed a sensitivity analysis by considering the proportion (0–1) of days stably housed and fitting a fractional logistic model. The fractional logistic model, which uses a quasi-likelihood function for estimation, was introduced by Papke and Woolridge (1996) [For the first objective, for each group, the adjusted change from baseline to 24-months follow-up was estimated by mean differences and 95% confidence intervals (continuous outcomes), and rate ratios and 95% confidence intervals (count outcomes). We fit models that included treatment group (fixed effect, HF vs TAU), categorical time (24-months vs baseline), interaction of treatment x time, and study city and need level at baseline (high vs. moderate) as covariates.For the second objective, in a more detailed examination of possible differential effect over time, we tested for differences between HF and TAU at For the third objective, the differences between HF and TAU were no longer the focus. Rather we took advantage of the large sample of women in a study on homelessness to identify predictors of our outcomes. To accomplish this we expanded the models from the second objective and added the following baseline predictors: age at enrolment (continuous), education (1 = less than high school, 0 = high school or higher), duration of homelessness (1 = ≥3, 0 = <3 years), whether minor children were being supported by the participant (1 = yes, 0 = no), level of suicidality (1 = moderate or high, 0 = mild or none), and high level of ACEs at baseline (1 = ≥5, 0 = <5 ACEs). These predictors were chosen because they represent a knowledge gap or have yielded inconsistent findings on longitudinal studies of women experiencing homelessness. We were unable to include ethnicity or Indigenous identity due to multicollinearity with study city.Multiple imputation with chained equations (MICE) was used to handle missing data from loss to follow-up, withdrawal, skipped interviews, nonresponse on specific items, and systematically measured lack of interviewer confidence in participant responses. We imputed all outcomes simultaneously and MICE imputation models included all variables needed to address three objectives [Data were imputed using Stata software (mi impute chained, Stata Statistical Software: Release 13. College Station, TX: StataCorp LP) and analyzed using SAS (PROC MIXED, GENMOD, GLIMMIX, PROC MIANALYZE, SAS 9.4, SAS Institute Inc, Cary, NC). SAS Syntax is provided in S2 Table in 