Sample and Data description
The current investigation will analyze the outcomes of 61 study participants across five timepoints (baseline, 6 months, 12 months, 18 months, and 24 months). Participants were interviewed five times over 24 months, with interviews occurring every six months (baseline, 6-months, 12months, 18months, and 24 months. 51 participants received the treatment and belong to the treatment group while 10 participants did not receive the treatment and belong to the intervention group. The purpose of this study is to examine if there are any differences in the outcomes of participants in the treatment group versus those in the control group over time.
Data and Measures
Participant outcomes on 8 specific measures will be considered. Specific measures include a depression scale, scale of housing instability, scale of economic abuse, and a composite scale of abuse which includes 4 subscales: stalking, physical abuse, emotional abuse, and sexual abuse. The data also includes additional participant-level information to be added into estimated models as covariates.
Data has been cleaned, scales scores calculated, univariate analysis completed (i.e., skewness, kurtosis, and missingness have been examined), and transformed from wide to long format in preparation for longitudinal analyses.

Analysis Description
Longitudinal analyses. All longitudinal analyses should be conducted using the brms package in R 4.1. (R Core Team, 2021).
To address the research question, multilevel analysis hierarchical linear modeling (HLM) will be used to model outcome trajectories and compare changes across all five timepoints (baseline, 6-months, 12-months, 18-months, and 24-months) on all dependent variables.
In testing the long-term effects of treatment on safety, housing stability, and depression, an HLM analysis with three levels will be conducted for each dependent variable. Level-1 time variant predictors included will be at the assessment level (e.g., timepoint of interview). Linear, quadratic, cubic, and higher polynomial terms will be included to delineate changes more clearly over time, if needed. Level-2 variables will include the person-level time invariant predictors and IPW estimates that may impact outcome trajectories. Finally, Level-3 will include variables at the organizational level and the type of service received to test the significance of trajectory differences between those who received treatment and those who did not receive treatment. Model building will apply a step-up strategy which will begin with an empty model (i.e., a model without predictors) and gradually add potential predictors pertaining to each of the levels. The final model selection will be based on the best-fit model generated from calculating and comparing the Loo Information Criterion (LOOIC) and the Watanabe-Akaike information criterion (WAIC) scores of several possible models using the loo package in R (Spiegelhalter et al., 2014).