Purrble RCT Entire Results with Write Up

Recording Keeping:

There are two master files that we are using for analyses. They are essentially the same file, though one is in wide format and the other is in long format.

The wide format dataset is called “Purrble_Master_Wide.” The long dataset format dataset is called “Purrble_Long_Master.” The wide dataset has all of the pre and posttest variables calculated, while the long does not. Otherwise, they do not differ.

This dataset includes the N=153 participants who were included in the randomized control trial examining Purrble with a population of university students. All participants were members of the LGTBQ+ community.

We use the “final” datasets in which we removed participant C72, who had no information on gender identity.

Preliminary Analyses

Sample Characteristics

These tables report the count of participants by condition, identity group, and by condition x identity group.

Table 1: Number of Participants by Condition

condition	Count
Purrble Treatment	76
Waitlist Control	77
Total	153

Table 2: Number of Participants by Gender Identity

identity_group	Count
Cisgender	76
Transgender	77
Total	153

Table 3: Cross-tabulation of Condition by Gender Identity

condition	Cisgender	TGD
Purrble Treatment	39	37
Waitlist Control	37	40

Age: Descriptives and Check for Baseline differences

Summarizes age (Mean, SD, Min, Max) by condition and runs a t-test comparing age by condition.

Table: Descriptive Statistics for Age by Condition (APA Format)

condition	Mean	SD	Min	Max
Purrble Treatment	20.44	2.29	16.00	25.00
Waitlist Control	20.09	2.46	16.00	25.00

Dependent Variable	t	df	p	d	95% CI
age	0.92	151.17	.361	0.15	[-0.17, 0.46]

Race, Nationality, and Sexual Orientation Descriptives

Sexual Orientation- Simplified

Table X. Simplified Sexual Orientation by Condition (n, %)

Sexual Orientation	Waitlist (n, %)	Purrble (n, %)	Total (n, %)
asexual	9 (11.7%)	13 (17.1%)	22 (14.4%)
bisexual	25 (32.5%)	28 (36.8%)	53 (34.6%)
demisexual	1 (1.3%)	2 (2.6%)	3 (2%)
gay/lesbian	18 (23.4%)	11 (14.5%)	29 (19%)
heterosexual	0 (0%)	1 (1.3%)	1 (0.7%)
pansexual	9 (11.7%)	8 (10.5%)	17 (11.1%)
queer	15 (19.5%)	13 (17.1%)	28 (18.3%)

Nationality

Table: Nationality by Condition (Counts and Percentages)

Nationality	Waitlist Control	Purrble Treatment	Total
bangladeshi	1 (1.3%)	0 (0%)	1 (0.7%)
british	36 (46.8%)	34 (44.7%)	70 (45.8%)
british-carribean	1 (1.3%)	1 (1.3%)	2 (1.3%)
british-indian	0 (0%)	1 (1.3%)	1 (0.7%)
british-japanese	1 (1.3%)	0 (0%)	1 (0.7%)
british-pakistani	1 (1.3%)	0 (0%)	1 (0.7%)
chinese	5 (6.5%)	1 (1.3%)	6 (3.9%)
filipino	0 (0%)	1 (1.3%)	1 (0.7%)
indian	5 (6.5%)	3 (3.9%)	8 (5.2%)
indonesian	1 (1.3%)	0 (0%)	1 (0.7%)
iranian	1 (1.3%)	0 (0%)	1 (0.7%)
irish	1 (1.3%)	1 (1.3%)	2 (1.3%)
irish-american	0 (0%)	1 (1.3%)	1 (0.7%)
irish-carribean	1 (1.3%)	0 (0%)	1 (0.7%)
malaysian chinese	1 (1.3%)	0 (0%)	1 (0.7%)
mexican	0 (0%)	1 (1.3%)	1 (0.7%)
nr	20 (26%)	29 (38.2%)	49 (32%)
pakistani	0 (0%)	1 (1.3%)	1 (0.7%)
polish	2 (2.6%)	2 (2.6%)	4 (2.6%)

Race

Table: Race Counts and Percentages by Condition

Race	Purrble Treatment		Waitlist Control		Total
Race	count_Purrble Treatment	percentage_Purrble Treatment	count_Waitlist Control	percentage_Waitlist Control	total_count	total_percentage
Race_Arabic	0	0.0	1	1.3	1	0.7
Race_Asian	10	13.2	17	22.1	27	17.6
Race_Black	1	1.3	3	3.9	4	2.6
Race_Hispanic	2	2.6	0	0.0	2	1.3
Race_White	60	78.9	55	71.4	115	75.2
Race_unknown	9	11.8	5	6.5	14	9.2

5 people in the Purrble Treatment condition reported multiple racial identities.
4 people in the Waitlist Control condition reported multiple racial identities.

Participation Over Time

Note: Weeks 1-3 were considered “pre-test.” Purrble was given (or not) after week 3. Weeks 11-13 are considered “Post-test”. ### Participation in Each Week over Time Analyses for the entire study and by treatment condition. Note: Something wonky in the table broken down by condition where Week 4 appears out of order- I don’t know why. The data is accurate.

### **Number of Participants in Each Condition**

Participant Counts by Condition

Condition	N
Purrble	76
Waitlist Control	77

### **Completion Counts Over Time**

Number of Participants Completing Each Week

Week	Count
1	146
2	148
3	149
4	141
5	138
6	138
7	138
8	141
9	126
10	128
11	128
12	117
13	130

### **Completion Counts by Week and Condition**

Number of Participants Completing Each Week (Columns: Weeks 1–13; Rows: Conditions)

Condition	1	2	3	5	6	7	8	9	10	12	13	4	11
Purrble	73	74	75	68	67	68	68	60	63	50	62	71	62
Waitlist Control	73	74	74	70	71	70	73	66	65	67	68	70	66

Follow-Up: Differences in Slope between the Two Groups Over Time

We examined whether the rate of decline in weekly completion counts differed between the Purrble and Waitlist Control groups by fitting a linear regression on aggregated counts (Count) with predictors Week (centered at Week 0), Condition (Waitlist Control = 0, Purrble = 1), and their interaction (Week × Condition). The interaction term (Week × Condition) was significant, B = −0.87, SE = 0.31, p = .009, indicating that the Purrble group’s weekly decline (approximately −1.52 participants per week) was significantly greater than in the Waitlist Control group (−0.65 participants per week).

### **Linear Model: Count ~ Week × Condition**

Regression Coefficients for Count ~ Week * Condition

Term	Estimate	Std. Error	p-value
(Intercept)	74.3076923	1.7131218	0.0000000
Week	-0.6483516	0.2158331	0.0065345
conditionPurrble	2.5769231	2.4227201	0.2990240
Week:conditionPurrble	-0.8736264	0.3052340	0.0090576

### **Interaction Term (Difference in Slope)**

Week:conditionPurrble — Slope Difference (Purrble vs Waitlist)

Term	Estimate	Std. Error	p-value
Week:conditionPurrble	-0.8736264	0.305234	0.0090576

**Interpretation:**
The Week × condition interaction is statistically significant (p = 0.00906 ), indicating that the slope of completion counts over time differs between conditions.

Descriptives in Number of Sessions Attended

Descriptives of number of sessions attended by condition and gender identity group.

Table 2: Overall Total Sessions Attended

mean_sessions	sd_sessions
12.60784	2.155883

Table 3: Total Sessions Attended by Condition

condition	mean_sessions	sd_sessions	n
0	12.85714	2.056532	77
1	12.35526	2.237284	76

Table 4: Total Sessions Attended by Gender Identity

identity_group	mean_sessions	sd_sessions	n
0	12.53947	2.193571	76
1	12.67532	2.130243	77

Table 5: Total Sessions Attended by Condition and Gender Identity

condition	identity_group	mean_sessions	sd_sessions	n
0	0	13.13514	1.417395	37
0	1	12.60000	2.499231	40
1	0	11.97436	2.630661	39
1	1	12.75676	1.673410	37

Attrition Analysis

Attrition is defined here as not having attended any post-test session (i.e., no attendance during Weeks 11–13). We create a binary indicator for post-test completion (1 = attended at least one post-test session, 0 = none) and calculate attrition rates overall, by condition and by gender identity. We used a chi-square test to determine if attrition differed by condition; it did not. ### Attrition Analysis by Condition The conditions did not significantly differ on any of the baseline measures of outcomes or by age. Attrition rates were low across both conditions, with 9.2% of participants in the Purrble condition and 6.5% in the Waitlist Control condition not completing the study. Attrition did not differ by condition, χ²(1) = 0.11, p = .75, or by gender identity, χ²(1) < 0.01, p = 1.

Chi-square test for differences in attrition by condition:

    Pearson's Chi-squared test with Yates' continuity correction

data:  attrition_ct
X-squared = 0.10517, df = 1, p-value = 0.7457

Table 7: Attrition Rate by Condition (with Completed and Not Completed counts)

condition	n	Completed	Not_Completed	attrition_rate	attrition_percent
0	77	72	5	0.0649351	6.5
1	76	69	7	0.0921053	9.2

Attrition by Gender Identity

No differences!

Chi-square test for differences in attrition by gender identity:

    Pearson's Chi-squared test with Yates' continuity correction

data:  attrition_ct
X-squared = 1.4323e-30, df = 1, p-value = 1

Table 8: Attrition Rate by Gender Identity (with Completed and Not Completed counts)

identity_group	n	Completed	Not_Completed	attrition_rate	attrition_percent
0	76	70	6	0.0789474	7.9
1	77	71	6	0.0779221	7.8

Attrition by Baseline Level of the Outcomes

In this section, we examined whether baseline scores on key outcome measures were associated with either condition or attrition status, or whether the effects of these two factors interacted. Loneliness was significant; follow-up below

Two-way ANOVA results for Pre_DERS8_Sum :

Two-way ANOVA for Pre_DERS8_Sum by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	7.983	7.983	0.356	0.552
attrition_status	1	30.432	30.432	1.356	0.246
condition:attrition_status	1	2.561	2.561	0.114	0.736
Residuals	148	3320.444	22.435	NA	NA

Two-way ANOVA results for Pre_GAD7_Sum :

Two-way ANOVA for Pre_GAD7_Sum by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	0.658	0.658	0.041	0.841
attrition_status	1	1.190	1.190	0.073	0.787
condition:attrition_status	1	0.001	0.001	0.000	0.994
Residuals	148	2401.630	16.227	NA	NA

Two-way ANOVA results for Pre_PHQ9_Sum :

Two-way ANOVA for Pre_PHQ9_Sum by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	18.249	18.249	0.859	0.356
attrition_status	1	2.796	2.796	0.132	0.717
condition:attrition_status	1	4.207	4.207	0.198	0.657
Residuals	148	3144.123	21.244	NA	NA

Two-way ANOVA results for Pre_SHS_Pathways :

Two-way ANOVA for Pre_SHS_Pathways by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	35.106	35.106	1.907	0.169
attrition_status	1	3.918	3.918	0.213	0.645
condition:attrition_status	1	25.587	25.587	1.390	0.240
Residuals	144	2651.435	18.413	NA	NA

Two-way ANOVA results for Pre_SHS_Agency :

Two-way ANOVA for Pre_SHS_Agency by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	34.935	34.935	1.450	0.231
attrition_status	1	8.541	8.541	0.354	0.553
condition:attrition_status	1	79.905	79.905	3.315	0.071
Residuals	144	3470.489	24.101	NA	NA

Two-way ANOVA results for Pre_SHS_TotalHope :

Two-way ANOVA for Pre_SHS_TotalHope by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	140.081	140.081	2.039	0.155
attrition_status	1	24.029	24.029	0.350	0.555
condition:attrition_status	1	195.924	195.924	2.852	0.093
Residuals	144	9893.938	68.708	NA	NA

Two-way ANOVA results for Pre_ucla_Sum :

Two-way ANOVA for Pre_ucla_Sum by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	3.945	3.945	1.556	0.214
attrition_status	1	1.318	1.318	0.520	0.472
condition:attrition_status	1	13.182	13.182	5.199	0.024
Residuals	143	362.575	2.535	NA	NA

Two-way ANOVA results for Pre_pmerq_Focus_Avg :

Two-way ANOVA for Pre_pmerq_Focus_Avg by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	1.392	1.392	1.243	0.267
attrition_status	1	2.233	2.233	1.995	0.160
condition:attrition_status	1	1.281	1.281	1.144	0.287
Residuals	144	161.212	1.120	NA	NA

Two-way ANOVA results for Pre_pmerq_Distract_Avg :

Two-way ANOVA for Pre_pmerq_Distract_Avg by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	1.554	1.554	1.247	0.266
attrition_status	1	4.213	4.213	3.380	0.068
condition:attrition_status	1	0.038	0.038	0.031	0.861
Residuals	144	179.482	1.246	NA	NA

Two-way ANOVA results for Pre_pmerq_AD_Avg :

Two-way ANOVA for Pre_pmerq_AD_Avg by Condition and Attrition Status

term	df	sumsq	meansq	statistic	p.value
condition	1	1.472	1.472	1.762	0.186
attrition_status	1	3.145	3.145	3.766	0.054
condition:attrition_status	1	0.440	0.440	0.527	0.469
Residuals	144	120.256	0.835	NA	NA

NA

UCLA Loneliess Follow Up:

Results: Among Attriters, baseline loneliness was significantly higher in the Waitlist Control group compared to the Purrble group, t(143) = 2.51, p = .013. Among Completers, there was no significant difference in baseline loneliness scores by condition, t(143) = 0.58, p = .56.

attrition_status = Attriter:
 condition_factor emmean    SE  df lower.CL upper.CL
 Waitlist Control   8.25 0.796 143     6.68     9.82
 Purrble            5.67 0.650 143     4.38     6.95

attrition_status = Completer:
 condition_factor emmean    SE  df lower.CL upper.CL
 Waitlist Control   7.19 0.192 143     6.81     7.57
 Purrble            7.03 0.193 143     6.65     7.41

Confidence level used: 0.95 
attrition_status = Attriter:
 contrast                   estimate    SE  df t.ratio p.value
 Waitlist Control - Purrble    2.583 1.030 143   2.513  0.0131

attrition_status = Completer:
 contrast                   estimate    SE  df t.ratio p.value
 Waitlist Control - Purrble    0.159 0.272 143   0.584  0.5599

Cohen's d |        95% CI
-------------------------
0.10      | [-0.24, 0.43]

- Estimated using pooled SD.Cohen's d |       95% CI
------------------------
1.95      | [0.33, 3.48]

- Estimated using pooled SD.

Descriptive Statistics for Pre_ucla_Sum by Condition and Attrition Status
condition	attrition_status	N	Mean	SD
0	Attriter	5	8.25	0.96
0	Completer	72	7.19	1.35
1	Attriter	7	5.67	1.51
1	Completer	69	7.03	1.83
Note. Means and standard deviations for Pre_ucla_Sum across four groups defined by condition (Purrble, Waitlist Control) and attrition status (Completer, Attriter).

Simple Effects Analysis: Pre_ucla_Sum by Attrition Status within the Purrble Condition

Dependent Variable	t	df	p	d	95% CI
Pre_ucla_Sum	-2.09	6.38	.079	-0.75	[-1.60, 0.09]

Simple Effects Analysis: Pre_ucla_Sum by Attrition Status within the Waitlist Control Condition

Dependent Variable	t	df	p	d	95% CI
Pre_ucla_Sum	2.10	3.73	.109	0.79	[-0.23, 1.81]

Baseline Outcome Variables Analyses

Reliability

DERS-8 Cronbach’s α = 0.886 
GAD-7 Cronbach’s α = 0.87 
PHQ-9 Cronbach’s α = 0.859 
SHS Total Cronbach’s α = 0.867 
UCLA Loneliness Cronbach’s α = 0.767 
PMERQ-Engage Cronbach’s α = 0.869 

Descriptive Analyses

The table below shows Pre- and Post-Test Descriptives for Study Variables

### **Pre-Test Descriptive Statistics**

Descriptive Statistics for Pre-Test Data

	N	Mean	SD	Min	Max	Skewness	Kurtosis
Pre_DERS8_Sum	152	28.148	4.718	14.333	38.333	-0.419	-0.132
Pre_GAD7_Sum	152	13.715	3.990	3.000	22.000	-0.166	-0.457
Pre_PHQ9_Sum	152	15.044	4.581	3.000	26.667	-0.019	-0.098
Pre_SHS_Pathways	148	13.287	4.298	3.000	24.000	-0.132	-0.420
Pre_SHS_Agency	148	10.699	4.945	3.000	24.000	0.343	-0.657
Pre_SHS_TotalHope	148	23.986	8.352	8.000	46.000	0.286	-0.304
Pre_ucla_Sum	147	7.082	1.615	3.000	9.000	-0.499	-0.663
Pre_pmerq_Focus_Avg	148	2.737	1.063	1.000	6.000	0.420	-0.095
Pre_pmerq_Distract_Avg	148	4.233	1.123	1.000	6.000	-0.857	0.698
Pre_pmerq_AD_Avg	148	3.485	0.923	1.000	6.000	-0.334	0.520

### **Post-Test Descriptive Statistics**

Descriptive Statistics for Post-Test Data

	N	Mean	SD	Min	Max	Skewness	Kurtosis
Post_DERS8_Sum	141	26.972	7.343	8	40	-0.266	-0.835
Post_GAD7_Sum	141	12.613	4.994	1	22	-0.071	-0.771
Post_PHQ9_Sum	141	14.314	6.331	0	27	-0.004	-0.696
Post_SHS_Pathways	130	14.700	4.305	3	24	-0.266	-0.430
Post_SHS_Agency	130	12.646	5.228	3	24	-0.015	-0.855
Post_SHS_TotalHope	130	27.346	8.806	6	47	-0.058	-0.483
Post_ucla_Sum	130	6.785	1.698	3	9	-0.409	-0.678
Post_pmerq_Focus_Avg	129	3.008	1.185	1	6	0.289	-0.301
Post_pmerq_Distract_Avg	129	4.336	1.058	1	6	-1.127	1.635
Post_pmerq_AD_Avg	129	3.672	0.951	1	6	-0.334	0.951

Basleine Equivalence of Outcomes (t‑Tests):

We run independent samples t‑tests comparing the two conditions on each pre‑test variable using nice_t_test from rempsyc. This provides t‑statistics, degrees of freedom, p‑values, effect sizes (Cohen’s d), and confidence intervals, all formatted into an APA‑style table. Result: No differences by chance.

Outlier Detection and Visualization :

We first convert each pre‑test variable to z‑scores and flag any observations with an absolute z‑score greater than 3 as potential outliers. A summary table is created that lists the number of outliers for each variable. We then specifically inspect the outliers for the Pre_pmerq_Focus_Avg variable, which appears to have two cases exceeding our threshold. To better understand the distribution of Pre_pmerq_Focus_Avg, we generate a boxplot (with jittered data points) that visually highlights the extreme values.

Summary of Potential Outliers (|z| > 3) for Pre-Test Variables:

Summary of Outliers for Pre-Test Variables (|z| > 3)

Variable	Outlier_Count
Pre_DERS8_Sum	0
Pre_GAD7_Sum	0
Pre_PHQ9_Sum	0
Pre_SHS_Pathways	0
Pre_SHS_Agency	0
Pre_SHS_TotalHope	0
Pre_ucla_Sum	0
Pre_pmerq_Focus_Avg	2
Pre_pmerq_Distract_Avg	0
Pre_pmerq_AD_Avg	0

Outliers for Pre_pmerq_Focus_Avg (|z| > 3):

Outliers for Pre_pmerq_Focus_Avg

psid	Pre_pmerq_Focus_Avg	z
C57	6	3.069197
C79	6	3.069197

Main Effects Analyses

We fit linear regression models to examine the effect of condition (coded as 1 = Purrble, 0 = Waitlist Control) on post-test outcomes, controlling for baseline levels of the outcome, gender identity (numeric), and age. DERS-8: Participants in the Purrble condition reported significantly better outcomes at post-test PPMERQ-AD: A significant positive effect of condition was found PHQ-9: The Purrble group showed lower depressive symptoms at post-test GAD-7: The condition effect was also significant, though smaller, favoring Purrble condition.

Dependent Variable	Predictor	df	b	t	p	sr2	95% CI
Post_DERS8_Sum	condition_num	135	-3.04	-3.20	.002**	.04	[0.00, 0.09]
	Pre_DERS8_Sum	135	0.92	9.21	< .001***	.35	[0.23, 0.48]
	identity_group_num	135	1.69	1.72	.088	.01	[0.00, 0.04]
	age	135	0.13	0.60	.549	.00	[0.00, 0.01]
Post_pmerq_Focus_Avg	condition_num	121	0.31	1.96	.052	.02	[0.00, 0.05]
	Pre_pmerq_Focus_Avg	121	0.73	9.40	< .001***	.39	[0.26, 0.52]
	identity_group_num	121	-0.27	-1.61	.110	.01	[0.00, 0.04]
	age	121	0.02	0.45	.654	.00	[0.00, 0.01]
Post_pmerq_Distract_Avg	condition_num	121	0.25	1.49	.138	.01	[0.00, 0.05]
	Pre_pmerq_Distract_Avg	121	0.48	6.48	< .001***	.25	[0.12, 0.38]
	identity_group_num	121	0.20	1.19	.238	.01	[0.00, 0.04]
	age	121	0.02	0.64	.526	.00	[0.00, 0.02]
Post_pmerq_AD_Avg	condition_num	121	0.30	2.28	.024*	.02	[0.00, 0.06]
	Pre_pmerq_AD_Avg	121	0.70	9.54	< .001***	.42	[0.29, 0.55]
	identity_group_num	121	-0.04	-0.32	.747	.00	[0.00, 0.01]
	age	121	0.03	1.06	.290	.01	[0.00, 0.02]
Post_GAD7_Sum	condition_num	135	-1.35	-2.04	.044*	.02	[0.00, 0.05]
	Pre_GAD7_Sum	135	0.74	8.98	< .001***	.35	[0.23, 0.48]
	identity_group_num	135	0.75	1.08	.281	.01	[0.00, 0.02]
	age	135	0.27	1.84	.068	.01	[0.00, 0.05]
Post_PHQ9_Sum	condition_num	135	-2.60	-3.64	< .001***	.04	[0.00, 0.09]
	Pre_PHQ9_Sum	135	1.00	12.96	< .001***	.53	[0.42, 0.65]
	identity_group_num	135	0.25	0.34	.734	.00	[0.00, 0.00]
	age	135	0.29	1.86	.064	.01	[0.00, 0.03]
Post_SHS_Pathways	condition_num	122	0.09	0.14	.889	.00	[0.00, 0.00]
	Pre_SHS_Pathways	122	0.46	6.04	< .001***	.21	[0.09, 0.34]
	identity_group_num	122	-0.84	-1.19	.237	.01	[0.00, 0.04]
	age	122	-0.28	-1.86	.065	.02	[0.00, 0.06]
Post_SHS_Agency	condition_num	122	0.44	0.53	.595	.00	[0.00, 0.01]
	Pre_SHS_Agency	122	0.53	6.57	< .001***	.26	[0.13, 0.39]
	identity_group_num	122	-0.47	-0.55	.582	.00	[0.00, 0.01]
	age	122	-0.17	-0.96	.337	.01	[0.00, 0.03]
Post_SHS_TotalHope	condition_num	122	0.62	0.46	.648	.00	[0.00, 0.01]
	Pre_SHS_TotalHope	122	0.53	6.71	< .001***	.26	[0.13, 0.39]
	identity_group_num	122	-1.16	-0.82	.414	.00	[0.00, 0.02]
	age	122	-0.43	-1.45	.151	.01	[0.00, 0.04]
Post_ucla_Sum	condition_num	121	-0.09	-0.40	.688	.00	[0.00, 0.01]
	Pre_ucla_Sum	121	0.70	10.02	< .001***	.43	[0.30, 0.56]
	identity_group_num	121	0.52	2.20	.030*	.02	[0.00, 0.06]
	age	121	0.11	2.12	.036*	.02	[0.00, 0.05]

Main Effects without outliers

Model Summary (Full Dataset):

Call:
lm(formula = Post_pmerq_Focus_Avg ~ condition_num + Pre_pmerq_Focus_Avg + 
    identity_group_num + age, data = Purrble_Master_Wide)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.16585 -0.64258 -0.05799  0.42448  2.73318 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)          0.67215    0.93052   0.722   0.4715    
condition_num        0.31072    0.15864   1.959   0.0525 .  
Pre_pmerq_Focus_Avg  0.73177    0.07788   9.396 4.43e-16 ***
identity_group_num  -0.27202    0.16888  -1.611   0.1098    
age                  0.01586    0.03528   0.450   0.6538    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8845 on 121 degrees of freedom
  (27 observations deleted due to missingness)
Multiple R-squared:  0.4612,    Adjusted R-squared:  0.4434 
F-statistic: 25.89 on 4 and 121 DF,  p-value: 1.635e-15


Model Summary (Outliers Removed):

Call:
lm(formula = Post_pmerq_Focus_Avg ~ condition_num + Pre_pmerq_Focus_Avg + 
    identity_group_num + age, data = Purrble_Master_Wide_no_outliers)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.14889 -0.64074 -0.06666  0.43406  2.70464 

Coefficients:
                    Estimate Std. Error t value Pr(>|t|)    
(Intercept)          0.72091    0.95012   0.759   0.4495    
condition_num        0.31636    0.16113   1.963   0.0519 .  
Pre_pmerq_Focus_Avg  0.71604    0.08537   8.388 1.17e-13 ***
identity_group_num  -0.26936    0.17004  -1.584   0.1158    
age                  0.01469    0.03567   0.412   0.6812    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.8902 on 119 degrees of freedom
  (27 observations deleted due to missingness)
Multiple R-squared:  0.4078,    Adjusted R-squared:  0.3879 
F-statistic: 20.48 on 4 and 119 DF,  p-value: 7.335e-13


Influential Observations in the Full Model (Cook's Distance > 0.027):
[1] "C15" "C16" "C17" "C47" "C71" "T15" "T22" "T31" "T48"

Comparison of Model Estimates for Post_pmerq_Focus_Avg

	Model Number	Dependent Variable	Predictor	df	b	t	p	sr2	CI_lower	CI_upper
Full1	1	Post_pmerq_Focus_Avg	condition_num	121	0.311	1.959	0.052	0.017	0.000	0.051
Full2	1	Post_pmerq_Focus_Avg	Pre_pmerq_Focus_Avg	121	0.732	9.396	0.000	0.393	0.263	0.523
Full3	1	Post_pmerq_Focus_Avg	identity_group_num	121	-0.272	-1.611	0.110	0.012	0.000	0.039
Full4	1	Post_pmerq_Focus_Avg	age	121	0.016	0.450	0.654	0.001	0.000	0.009
No Outliers1	2	Post_pmerq_Focus_Avg	condition_num	119	0.316	1.963	0.052	0.019	0.000	0.057
No Outliers2	2	Post_pmerq_Focus_Avg	Pre_pmerq_Focus_Avg	119	0.716	8.388	0.000	0.350	0.218	0.483
No Outliers3	2	Post_pmerq_Focus_Avg	identity_group_num	119	-0.269	-1.584	0.116	0.012	0.000	0.043
No Outliers4	2	Post_pmerq_Focus_Avg	age	119	0.015	0.412	0.681	0.001	0.000	0.009

Moderation Models for Main Effects

These models look at two questions: (1) Does the impact of condition depend on participants’ baseline level of that outcome? and (2) Does the impact of condition differ for TGD vs. cis participants? We find significant moderation by gender identity for DERS-8 and GAD-7; none for baseline version of the outcome.

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_DERS8_Sum	condition_num	134	-0.21	-3.17	.002**	.04	[0.00, 0.09]
	Pre_DERS8_Sum	134	0.60	9.18	< .001***	.35	[0.23, 0.48]
	identity_group_num	134	0.12	1.71	.089	.01	[0.00, 0.04]
	age	134	0.04	0.53	.595	.00	[0.00, 0.01]
	condition_num × Pre_DERS8_Sum	134	-0.04	-0.65	.517	.00	[0.00, 0.01]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_Focus_Avg	condition_num	120	0.13	1.93	.056	.02	[0.00, 0.05]
	Pre_pmerq_Focus_Avg	120	0.65	9.35	< .001***	.39	[0.26, 0.52]
	identity_group_num	120	-0.13	-1.74	.085	.01	[0.00, 0.04]
	age	120	0.03	0.49	.625	.00	[0.00, 0.01]
	condition_num × Pre_pmerq_Focus_Avg	120	-0.07	-1.02	.309	.00	[0.00, 0.02]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_Distract_Avg	condition_num	120	0.11	1.45	.150	.01	[0.00, 0.05]
	Pre_pmerq_Distract_Avg	120	0.52	6.50	< .001***	.25	[0.12, 0.38]
	identity_group_num	120	0.10	1.18	.241	.01	[0.00, 0.04]
	age	120	0.06	0.66	.510	.00	[0.00, 0.02]
	condition_num × Pre_pmerq_Distract_Avg	120	-0.05	-0.67	.505	.00	[0.00, 0.02]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_AD_Avg	condition_num	120	0.15	2.24	.027*	.02	[0.00, 0.06]
	Pre_pmerq_AD_Avg	120	0.67	9.45	< .001***	.42	[0.29, 0.55]
	identity_group_num	120	-0.03	-0.36	.722	.00	[0.00, 0.01]
	age	120	0.08	1.07	.288	.01	[0.00, 0.02]
	condition_num × Pre_pmerq_AD_Avg	120	-0.03	-0.38	.704	.00	[0.00, 0.01]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_DERS8_Sum	condition_num	134	-0.21	-3.23	.002**	.04	[0.00, 0.09]
	identity_group_num	134	0.12	1.75	.082	.01	[0.00, 0.04]
	Pre_DERS8_Sum	134	0.59	9.24	< .001***	.35	[0.23, 0.47]
	age	134	0.04	0.59	.558	.00	[0.00, 0.01]
	condition_num × identity_group_num	134	0.13	2.10	.038*	.02	[0.00, 0.05]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_Focus_Avg	condition_num	120	0.13	2.01	.046*	.02	[0.00, 0.05]
	identity_group_num	120	-0.11	-1.55	.124	.01	[0.00, 0.04]
	Pre_pmerq_Focus_Avg	120	0.68	9.65	< .001***	.41	[0.28, 0.54]
	age	120	0.03	0.48	.630	.00	[0.00, 0.01]
	condition_num × identity_group_num	120	0.12	1.79	.076	.01	[0.00, 0.04]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_Distract_Avg	condition_num	120	0.12	1.49	.139	.01	[0.00, 0.05]
	identity_group_num	120	0.10	1.19	.238	.01	[0.00, 0.04]
	Pre_pmerq_Distract_Avg	120	0.51	6.46	< .001***	.25	[0.12, 0.38]
	age	120	0.05	0.63	.528	.00	[0.00, 0.02]
	condition_num × identity_group_num	120	0.03	0.37	.708	.00	[0.00, 0.01]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_pmerq_AD_Avg	condition_num	120	0.16	2.31	.023*	.02	[0.00, 0.06]
	identity_group_num	120	-0.02	-0.30	.766	.00	[0.00, 0.01]
	Pre_pmerq_AD_Avg	120	0.68	9.65	< .001***	.43	[0.30, 0.56]
	age	120	0.08	1.09	.279	.01	[0.00, 0.02]
	condition_num × identity_group_num	120	0.09	1.30	.197	.01	[0.00, 0.03]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_GAD7_Sum	condition_num	134	-0.14	-2.03	.044*	.02	[0.00, 0.05]
	Pre_GAD7_Sum	134	0.59	8.85	< .001***	.35	[0.22, 0.47]
	identity_group_num	134	0.08	1.07	.284	.01	[0.00, 0.02]
	age	134	0.13	1.83	.069	.01	[0.00, 0.05]
	condition_num × Pre_GAD7_Sum	134	0.00	0.07	.941	.00	[0.00, 0.00]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_PHQ9_Sum	condition_num	134	-0.21	-3.64	< .001***	.04	[0.00, 0.09]
	Pre_PHQ9_Sum	134	0.73	12.94	< .001***	.53	[0.42, 0.64]
	identity_group_num	134	0.02	0.40	.687	.00	[0.00, 0.01]
	age	134	0.11	1.83	.070	.01	[0.00, 0.03]
	condition_num × Pre_PHQ9_Sum	134	-0.05	-0.88	.380	.00	[0.00, 0.01]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_GAD7_Sum	condition_num	134	-0.13	-2.05	.042*	.02	[0.00, 0.05]
	identity_group_num	134	0.08	1.12	.263	.01	[0.00, 0.02]
	Pre_GAD7_Sum	134	0.58	8.95	< .001***	.34	[0.22, 0.47]
	age	134	0.13	1.85	.067	.01	[0.00, 0.04]
	condition_num × identity_group_num	134	0.14	2.18	.031*	.02	[0.00, 0.06]

Dependent Variable	Predictor	df	b*	t	p	sr2	95% CI
Post_PHQ9_Sum	condition_num	134	-0.20	-3.64	< .001***	.04	[0.00, 0.09]
	identity_group_num	134	0.02	0.38	.706	.00	[0.00, 0.00]
	Pre_PHQ9_Sum	134	0.71	12.79	< .001***	.51	[0.39, 0.63]
	age	134	0.11	1.86	.065	.01	[0.00, 0.03]
	condition_num × identity_group_num	134	0.10	1.79	.076	.01	[0.00, 0.03]

Follow up: DERS 8

Since the interaction of condition by identity group was signifiacnt, I have to probe it using simple slopes.

Result:

For cisgender participants, controlling for pre‑test emotion regulation, condition significantly predicted post‑test scores, with the intervention yielding lower (i.e., better) scores (b = –4.90, SE = 1.41, t(67) = –3.47, p = .001, adjusted R² = .47). In contrast, for transgender/gender diverse participants, condition was not a significant predictor of post‑test emotion regulation (b = –1.07, SE = 1.23, t(67) = –0.87, p = .39, adjusted R² = .37). sad.

Call:
lm(formula = Post_DERS8_Sum ~ condition_num + Pre_DERS8_Sum, 
    data = filter(Purrble_Master_Wide, identity_group == "0"))

Residuals:
    Min      1Q  Median      3Q     Max 
-15.085  -3.353   1.433   3.929  14.517 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     4.8137     4.9268   0.977  0.33206    
condition_num  -4.9030     1.4137  -3.468  0.00092 ***
Pre_DERS8_Sum   1.0170     0.1502   6.771 3.89e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.885 on 67 degrees of freedom
  (6 observations deleted due to missingness)
Multiple R-squared:  0.484, Adjusted R-squared:  0.4686 
F-statistic: 31.43 on 2 and 67 DF,  p-value: 2.361e-10


Call:
lm(formula = Post_DERS8_Sum ~ condition_num + Pre_DERS8_Sum, 
    data = filter(Purrble_Master_Wide, identity_group == "1"))

Residuals:
     Min       1Q   Median       3Q      Max 
-12.1803  -2.3719   0.0348   3.7168  10.4756 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     6.1183     4.1405   1.478    0.144    
condition_num  -1.0671     1.2265  -0.870    0.387    
Pre_DERS8_Sum   0.8226     0.1274   6.456 1.41e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.13 on 67 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.3885,    Adjusted R-squared:  0.3703 
F-statistic: 21.29 on 2 and 67 DF,  p-value: 6.971e-08

Follow up: GAD 7

Since the interaction of condition by identity group was signifiacnt, I have to probe it using simple slopes. 0= Cisgender participants have significant condition effect 1=Transgender participants have no significant condition effect

Call:
lm(formula = Post_GAD7_Sum ~ condition_num + Pre_GAD7_Sum, data = filter(Purrble_Master_Wide, 
    identity_group == "0"))

Residuals:
    Min      1Q  Median      3Q     Max 
-9.9382 -2.9558 -0.6394  3.4989  9.1100 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     7.0008     2.4057   2.910  0.00490 ** 
condition_num  -2.7678     1.0084  -2.745  0.00777 ** 
Pre_GAD7_Sum    0.6950     0.1314   5.289 1.46e-06 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.211 on 67 degrees of freedom
  (6 observations deleted due to missingness)
Multiple R-squared:  0.3567,    Adjusted R-squared:  0.3375 
F-statistic: 18.57 on 2 and 67 DF,  p-value: 3.821e-07


Call:
lm(formula = Post_GAD7_Sum ~ condition_num + Pre_GAD7_Sum, data = filter(Purrble_Master_Wide, 
    identity_group == "1"))

Residuals:
    Min      1Q  Median      3Q     Max 
-8.2530 -2.1982  0.0676  2.7371  8.9484 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)     2.0787     1.9095   1.089    0.280    
condition_num   0.1055     0.8587   0.123    0.903    
Pre_GAD7_Sum    0.7715     0.1018   7.577 1.39e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.582 on 67 degrees of freedom
  (7 observations deleted due to missingness)
Multiple R-squared:  0.4635,    Adjusted R-squared:  0.4475 
F-statistic: 28.94 on 2 and 67 DF,  p-value: 8.721e-10

Self-Harm Analyses

Frequencies by Condition and Response over Time

Below, we display a table and graph of the frequency of responses for all self-harm questions, the frequency of flagged responses to each self-harm question over time, and the frequency of flagged responses to each self-harm question over time, separated by condition.

Self-Harm Logistic Regression

Post-test Logistic Regression to Investigate Intervention Effects on Self-Harm Outcomes Result: Condition was not a significant predictor of any self-harm outcome (coded binary).

Characteristic	SHQ1 Model		SHQ2 Model		SHQ3 Model		SHQ_Any Model
	OR1,2	SE2	OR1,2	SE2	OR1,2	SE2	OR1,2	SE2
condition
Purrble Treatment	—	—	—	—	—	—	—	—
Waitlist Control	0.87	0.452	1.02	0.412	1.15	0.546	0.91	0.434
SHQ1_2	11.6***	0.484
SHQ2_2			4.36***	0.408
SHQ3_2					3.14*	0.559
SHQ_Any_2							5.83***	0.486
1 *p<0.05; **p<0.01; ***p<0.001
2 OR = Odds Ratio, SE = Standard Error

Self-Harm Proportional Odds Regression

Frequencies Tables

**Frequencies for shqscreener1_w1 **

Response	Count	Percent
1	27	18.5
2	47	32.2
3	56	38.4
4	16	11.0

**Frequencies for shqscreener1_w12 **

Response	Count	Percent
1	47	40.2
2	29	24.8
3	34	29.1
4	7	6.0

**Frequencies for shqscreener2_w1 **

Response	Count	Percent
1	78	53.4
2	37	25.3
3	27	18.5
4	4	2.7

**Frequencies for shqscreener2_w12 **

Response	Count	Percent
1	70	59.8
2	27	23.1
3	15	12.8
4	5	4.3

**Frequencies for shqscreener3_w1 **

Response	Count	Percent
1	118	80.8
2	18	12.3
3	10	6.8

**Frequencies for shqscreener3_w12 **

Response	Count	Percent
1	100	85.5
2	12	10.3
3	5	4.3

Proportional Odds Models: Brant Tests

All six Brant tests (one for each screener at Week 1 and Week 12) produced non‐significant p‐values, indicating that the proportional‐odds (parallel regression) assumption holds in every case.

-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     1.8 2   0.41
condition1  1.8 2   0.41
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 1 at Week 1:"
                X2 df probability
Omnibus    1.80303  2   0.4059541
condition1 1.80303  2   0.4059541
-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     1.03    2   0.6
condition1  1.03    2   0.6
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 1 at Week 12:"
                 X2 df probability
Omnibus    1.031749  2   0.5969783
condition1 1.031749  2   0.5969783
-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     1.3 2   0.52
condition1  1.3 2   0.52
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 2 at Week 1:"
                 X2 df probability
Omnibus    1.303816  2   0.5210507
condition1 1.303816  2   0.5210507
-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     2.49    2   0.29
condition1  2.49    2   0.29
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 2 at Week 12:"
                 X2 df probability
Omnibus    2.493925  2   0.2873763
condition1 2.493925  2   0.2873763
-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     1.42    1   0.23
condition1  1.42    1   0.23
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 3 at Week 1:"
                 X2 df probability
Omnibus    1.417486  1   0.2338176
condition1 1.417486  1   0.2338176
-------------------------------------------- 
Test for    X2  df  probability 
-------------------------------------------- 
Omnibus     1.01    1   0.32
condition1  1.01    1   0.32
-------------------------------------------- 

H0: Parallel Regression Assumption holds
[1] "Brant Test for Screener 3 at Week 12:"
                 X2 df probability
Omnibus    1.005784  1    0.315915
condition1 1.005784  1    0.315915

No significant results of Purrble on self-harm using proprtional odds (ordinal data that maintains frequency)

Proportional Odds Regression Results Controlling for Age and Baseline Response (Week 1)

Model	term	estimate	std.error	odds_ratio	statistic	p.value
Screener 1	condition1	0.090	0.363	1.094	0.248	0.804
Screener 1	age	0.045	0.083	1.046	0.540	0.589
Screener 1	identity_group_num	0.595	0.375	1.813	1.587	0.113
Screener 1	shqscreener1_w1.L	1.856	0.486	6.400	3.822	0.000
Screener 1	shqscreener1_w1.Q	-0.115	0.404	0.891	-0.284	0.776
Screener 1	shqscreener1_w1.C	0.194	0.324	1.214	0.600	0.549
Screener 1	1|2	1.412	1.917	4.102	0.736	0.462
Screener 1	2|3	2.500	1.929	12.184	1.296	0.195
Screener 1	3|4	4.935	1.980	139.059	2.493	0.013
Screener 2	condition1	0.300	0.427	1.350	0.703	0.482
Screener 2	age	0.122	0.094	1.129	1.298	0.194
Screener 2	identity_group_num	1.406	0.448	4.082	3.138	0.002
Screener 2	shqscreener2_w1.L	3.213	0.750	24.862	4.285	0.000
Screener 2	shqscreener2_w1.Q	0.593	0.599	1.809	0.989	0.323
Screener 2	shqscreener2_w1.C	0.623	0.473	1.864	1.316	0.188
Screener 2	1|2	3.999	2.230	54.559	1.794	0.073
Screener 2	2|3	5.510	2.266	247.255	2.432	0.015
Screener 2	3|4	7.450	2.328	1719.687	3.200	0.001
Screener 3	condition1	0.098	0.551	1.103	0.178	0.859
Screener 3	age	0.001	0.125	1.001	0.011	0.991
Screener 3	identity_group_num	-0.140	0.566	0.869	-0.248	0.804
Screener 3	shqscreener3_w1.L	0.234	0.814	1.263	0.287	0.774
Screener 3	shqscreener3_w1.Q	-0.712	0.667	0.491	-1.067	0.286
Screener 3	1|2	1.407	2.836	4.082	0.496	0.620
Screener 3	2|3	2.698	2.858	14.846	0.944	0.345

Self-Harm Moderation Models: Gender Identity

No moderation effect of gender identity in proprtional odds models.

Proportional Odds Regression Moderation Results (Condition * Identity_Group_Num Interaction)

Model	term	estimate	std.error	odds_ratio	statistic	p.value
Screener 1	condition1	0.619	1.174	1.857	0.527	0.598
Screener 1	identity_group_num	0.752	0.502	2.121	1.499	0.134
Screener 1	age	0.046	0.083	1.048	0.556	0.578
Screener 1	shqscreener1_w1.L	1.836	0.489	6.269	3.756	0.000
Screener 1	shqscreener1_w1.Q	-0.148	0.411	0.862	-0.360	0.719
Screener 1	shqscreener1_w1.C	0.202	0.325	1.224	0.622	0.534
Screener 1	condition1:identity_group_num	-0.351	0.741	0.704	-0.474	0.636
Screener 1	1|2	1.687	2.007	5.404	0.840	0.401
Screener 1	2|3	2.777	2.020	16.071	1.375	0.169
Screener 1	3|4	5.207	2.066	182.494	2.520	0.012
Screener 2	condition1	0.214	1.369	1.239	0.157	0.876
Screener 2	identity_group_num	1.381	0.592	3.978	2.332	0.020
Screener 2	age	0.122	0.094	1.129	1.295	0.195
Screener 2	shqscreener2_w1.L	3.215	0.751	24.905	4.280	0.000
Screener 2	shqscreener2_w1.Q	0.590	0.602	1.803	0.980	0.327
Screener 2	shqscreener2_w1.C	0.619	0.477	1.857	1.296	0.195
Screener 2	condition1:identity_group_num	0.055	0.838	1.057	0.066	0.947
Screener 2	1|2	3.954	2.332	52.120	1.696	0.090
Screener 2	2|3	5.464	2.368	236.111	2.308	0.021
Screener 2	3|4	7.403	2.432	1640.376	3.043	0.002
Screener 3	condition1	-0.321	1.761	0.725	-0.182	0.855
Screener 3	identity_group_num	-0.264	0.752	0.768	-0.351	0.725
Screener 3	age	0.002	0.125	1.002	0.015	0.988
Screener 3	shqscreener3_w1.L	0.290	0.846	1.337	0.343	0.732
Screener 3	shqscreener3_w1.Q	-0.699	0.669	0.497	-1.044	0.296
Screener 3	condition1:identity_group_num	0.290	1.155	1.336	0.251	0.802
Screener 3	1|2	1.212	2.940	3.360	0.412	0.680
Screener 3	2|3	2.504	2.960	12.233	0.846	0.398

Supplementary Materials: Mixed Effects Models

To evaluate how outcomes changed over time and whether these changes differed by condition, we fit mixed-effects models for each of our primary outcome variables. These models account for both within-person change and between-person differences.

For each outcomem we ran a linear mixed-effects model using the lmer() function.

The models tested: Main effects of Week (time), condition, and their interaction Covariates: identity group and age A random intercept and slope for each participant ((Week & psid)), allowing each person to have their own baseline and rate of change over time

Emotion Reg was significant Depression significant Anxiety not significant (close to marginal p=.11- more evidence of unstable effect)

Mixed-Effects Model for DERS8_Sum with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	22.165	3.733	5.937	148.275	0.000	14.848	29.481
fixed	NA	Week	-0.265	0.064	-4.120	152.297	0.000	-0.391	-0.139
fixed	NA	conditionWaitlist Control	-0.105	0.828	-0.127	148.835	0.899	-1.729	1.518
fixed	NA	identity_groupTGD	0.930	0.824	1.129	148.251	0.261	-0.685	2.545
fixed	NA	age	0.277	0.174	1.588	147.721	0.114	-0.065	0.619
fixed	NA	Week:conditionWaitlist Control	0.284	0.090	3.152	148.644	0.002	0.108	0.461
ran_pars	psid	sd__(Intercept)	4.594	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.103	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.608	NA	NA	NA	NA	NA	NA

NULL

# R2 for Mixed Models

  Conditional R2: 0.717
     Marginal R2: 0.037

Mixed-Effects Model for DERS8_Sum with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	22.165	3.733	5.937	148.275	0.000	14.848	29.481
fixed	NA	Week	-0.265	0.064	-4.120	152.297	0.000	-0.391	-0.139
fixed	NA	conditionWaitlist Control	-0.105	0.828	-0.127	148.835	0.899	-1.729	1.518
fixed	NA	identity_groupTGD	0.930	0.824	1.129	148.251	0.261	-0.685	2.545
fixed	NA	age	0.277	0.174	1.588	147.721	0.114	-0.065	0.619
fixed	NA	Week:conditionWaitlist Control	0.284	0.090	3.152	148.644	0.002	0.108	0.461
ran_pars	psid	sd__(Intercept)	4.594	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.103	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.608	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.717
     Marginal R2: 0.037

Mixed-Effects Model for pmerq_Focus_Avg with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	3.943	0.738	5.345	149.531	0.000	2.497	5.389
fixed	NA	Week	0.048	0.012	4.139	125.908	0.000	0.025	0.070
fixed	NA	conditionWaitlist Control	0.258	0.188	1.372	143.494	0.172	-0.111	0.628
fixed	NA	identity_groupTGD	-0.476	0.163	-2.927	147.047	0.004	-0.794	-0.157
fixed	NA	age	-0.059	0.034	-1.705	146.966	0.090	-0.126	0.009
fixed	NA	Week:conditionWaitlist Control	-0.035	0.016	-2.192	129.157	0.030	-0.067	-0.004
ran_pars	psid	sd__(Intercept)	0.799	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	0.454	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.021	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.640	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.680
     Marginal R2: 0.060

Mixed-Effects Model for pmerq_Distract_Avg with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	5.349	0.709	7.543	151.365	0.000	3.959	6.739
fixed	NA	Week	0.031	0.013	2.307	135.818	0.023	0.005	0.057
fixed	NA	conditionWaitlist Control	0.265	0.202	1.310	145.068	0.192	-0.132	0.662
fixed	NA	identity_groupTGD	0.086	0.156	0.552	146.638	0.582	-0.219	0.391
fixed	NA	age	-0.066	0.033	-2.006	146.580	0.047	-0.131	-0.002
fixed	NA	Week:conditionWaitlist Control	-0.035	0.019	-1.849	137.700	0.067	-0.071	0.002
ran_pars	psid	sd__(Intercept)	0.906	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.412	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.057	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.648	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.650
     Marginal R2: 0.031

Mixed-Effects Model for pmerq_AD_Avg with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	4.685	0.625	7.501	150.411	0.000	3.461	5.909
fixed	NA	Week	0.040	0.010	4.079	252.556	0.000	0.021	0.059
fixed	NA	conditionWaitlist Control	0.261	0.161	1.622	160.864	0.107	-0.054	0.576
fixed	NA	identity_groupTGD	-0.202	0.138	-1.465	147.788	0.145	-0.471	0.068
fixed	NA	age	-0.064	0.029	-2.205	147.697	0.029	-0.121	-0.007
fixed	NA	Week:conditionWaitlist Control	-0.035	0.014	-2.568	254.123	0.011	-0.062	-0.008
ran_pars	psid	sd__(Intercept)	0.674	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	0.999	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.009	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.552	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.661
     Marginal R2: 0.042

Mixed-Effects Model for GAD7_Sum with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	10.890	2.892	3.766	149.580	0.000	5.222	16.558
fixed	NA	Week	-0.156	0.046	-3.411	153.831	0.001	-0.246	-0.066
fixed	NA	conditionWaitlist Control	-0.065	0.681	-0.095	149.312	0.924	-1.400	1.270
fixed	NA	identity_groupTGD	1.253	0.637	1.967	148.699	0.051	0.004	2.502
fixed	NA	age	0.110	0.135	0.815	148.162	0.416	-0.154	0.374
fixed	NA	Week:conditionWaitlist Control	0.103	0.064	1.608	148.732	0.110	-0.023	0.228
ran_pars	psid	sd__(Intercept)	3.702	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.240	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.293	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.220	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.606
     Marginal R2: 0.024

Mixed-Effects Model for PHQ9_Sum with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	14.141	3.462	4.085	148.102	0.000	7.356	20.926
fixed	NA	Week	-0.177	0.048	-3.705	153.199	0.000	-0.271	-0.083
fixed	NA	conditionWaitlist Control	-1.216	0.753	-1.614	148.674	0.109	-2.692	0.261
fixed	NA	identity_groupTGD	1.630	0.764	2.133	148.275	0.035	0.132	3.127
fixed	NA	age	0.038	0.162	0.234	147.817	0.816	-0.279	0.355
fixed	NA	Week:conditionWaitlist Control	0.222	0.067	3.320	148.205	0.001	0.091	0.353
ran_pars	psid	sd__(Intercept)	4.187	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	0.056	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.313	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.262	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.703
     Marginal R2: 0.024

Mixed-Effects Model for SHS_Pathways with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	18.228	2.760	6.604	153.499	0.000	12.818	23.638
fixed	NA	Week	0.180	0.053	3.423	139.625	0.001	0.077	0.283
fixed	NA	conditionWaitlist Control	0.879	0.807	1.088	148.196	0.278	-0.704	2.461
fixed	NA	identity_groupTGD	-1.888	0.605	-3.122	148.071	0.002	-3.074	-0.703
fixed	NA	age	-0.246	0.128	-1.924	148.121	0.056	-0.497	0.005
fixed	NA	Week:conditionWaitlist Control	-0.058	0.074	-0.783	141.089	0.435	-0.202	0.087
ran_pars	psid	sd__(Intercept)	3.517	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.431	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.201	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	2.669	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.630
     Marginal R2: 0.072

Mixed-Effects Model for SHS_Agency with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	11.036	3.221	3.426	151.999	0.001	4.723	17.350
fixed	NA	Week	0.239	0.063	3.810	135.590	0.000	0.116	0.361
fixed	NA	conditionWaitlist Control	0.986	0.897	1.099	144.887	0.274	-0.773	2.745
fixed	NA	identity_groupTGD	-1.511	0.707	-2.136	147.876	0.034	-2.897	-0.124
fixed	NA	age	-0.045	0.150	-0.300	147.892	0.765	-0.338	0.249
fixed	NA	Week:conditionWaitlist Control	-0.069	0.088	-0.782	136.888	0.435	-0.240	0.103
ran_pars	psid	sd__(Intercept)	3.946	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.349	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.294	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	2.928	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.669
     Marginal R2: 0.051

Mixed-Effects Model for SHS_TotalHope with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	29.159	5.488	5.313	152.155	0.000	18.402	39.915
fixed	NA	Week	0.419	0.103	4.076	138.799	0.000	0.217	0.620
fixed	NA	conditionWaitlist Control	1.843	1.525	1.209	146.500	0.229	-1.146	4.831
fixed	NA	identity_groupTGD	-3.422	1.205	-2.840	147.951	0.005	-5.784	-1.060
fixed	NA	age	-0.285	0.255	-1.118	148.046	0.265	-0.785	0.215
fixed	NA	Week:conditionWaitlist Control	-0.125	0.144	-0.869	139.873	0.386	-0.406	0.157
ran_pars	psid	sd__(Intercept)	7.134	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.419	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.522	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	4.604	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.714
     Marginal R2: 0.070

Mixed-Effects Model for ucla_Sum with 95% CI

effect	group	term	estimate	std.error	statistic	df	p.value	2.5 %	97.5 %
fixed	NA	(Intercept)	6.511	1.162	5.602	150.166	0.000	4.232	8.789
fixed	NA	Week	-0.028	0.017	-1.668	134.259	0.098	-0.060	0.005
fixed	NA	conditionWaitlist Control	0.301	0.295	1.019	144.435	0.310	-0.278	0.880
fixed	NA	identity_groupTGD	0.498	0.256	1.948	146.945	0.053	-0.003	1.000
fixed	NA	age	0.013	0.054	0.240	147.172	0.810	-0.093	0.119
fixed	NA	Week:conditionWaitlist Control	-0.008	0.023	-0.366	136.105	0.715	-0.054	0.037
ran_pars	psid	sd__(Intercept)	1.389	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.052	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.045	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	0.888	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.729
     Marginal R2: 0.030