The power analyses were conducted using the Monte Carlo simulation method for the Primary Aim and Secondary Aim 1 and using GPower program for Secondary Aim 2. We assumed an overall attrition rate of 15% when calculating the power. The MPI’s ongoing study testing the effect of housing support on homeless mothers reveals medium effect size in reducing depressive symptoms (
d = .59), favoring the housing intervention over treatment as usual (TAU)/assessment only. Few studies examined the effect of housing on suicidality; a recent observational study reported a small effect size from baseline to 2-year follow-up [
27]. Given the large difference across studies and that the proposed study tests housing support against an active intervention, and the differences between the two conditions may be smaller than that between housing support and TAU, we assumed small-to-medium effect sizes when conducting the power analysis. For the Primary Aim, with dichotomous predictors (contrasts between intervention conditions) that have regression coefficients of .15 (small-to-medium effect size) for the slopes of growth factors [
56], a sample size of 240 can produce a power of .86 to detect the housing effect on the growth rate of outcomes. For Secondary Aim 1, the MPI’s clinical trial of housing support suggested a large effect size (
d = 1.26) in improving housing stability and a medium effect size in reducing substance use (
d = .49). Similarly, a meta-analysis reported large effect sizes (
d = 1.24 on average) of Housing First approaches in increasing housing stability [
57]. Thus, we assumed a medium effect size for the intervention-to-mediator paths and a small-to-medium effect size for the mediator-to-outcome paths. Following the model specification suggested by Thoemmes et al. (2010) [
58], the proposed sample size could provide a power of .91 to detect mediating effects for models with one mediator and a power of .82 for the serial mediation models with two mediators. For Secondary Aim 2, assuming a small-to-medium effect size (i.e.,
f = .20), the power to detect a group difference in an RMANOVA with 5 repeated measurements is .84. For the GLMM, to achieve 80% power, the effect size of the group differences in the slope needs to be of medium size (regression coefficient of .20). A smaller than medium effect size will not provide sufficient power to detect housing effect on suicidal attempts. However, our goal is to estimate an effect size that can be used to guide sample-size estimates for a future fully-powered study.