Purrble RCT Analyses: Revise and Resubmit

install.packages(“rciplot”) # 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.

These analyses were conducted in October by Aubrey Rhodes. We use the “final” datasets in which we removed participant C72, who had no information on gender identity.

These analyses remove all of the variables except for emotion regulation, PHQ, and Anxiety as outcomes.

2.1. Participants

2.1.1 Participant Disposition

Corresponding Text: “resulting in a final sample size of 153 participants: Purrble condition (n=76), and the waitlist control condition (n=77).”

“Gender identity was evenly distributed across conditions, with 76 participants (49.7%) identifying as cisgender and 77 identifying as transgender, gender non-conforming, or questioning and or gender diverse (TGD; (50.3%).”

“Within conditions, the Purrble group consisted of 39 cisgender participants and 37 TGD participants, while the waitlist control group consisted of 37 cisgender participants and 40 TGD participants.”

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	Transgender
Purrble Treatment	39	37
Waitlist Control	37	40

2.1.2 Participant Characteristics

Participants characteristics including sexual orientation, race/ethnicity, and age are shown reported by condition in Table 1.

Age: Descriptives

Summarizes age (Mean, SD, Min, Max) by condition.

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

condition	Mean	SD	Min	Max
Purrble Treatment	20.42	2.29	16.00	25.00
Waitlist Control	20.09	2.46	16.00	25.00

Sexual Orientation- Simplified

Table: Sexual Orientation (so_simplified) by Condition (Counts and Percentages)

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

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.

2.1.3 Engagement and Retention

Number of questionnaires

Results Text: Participants completed an average of 12.4 questionnaires in the Purrble and 12.9 questionnaires in the control condition out of a possible 14 (Baseline [“Week 0”] through Follow-Up [“Week 13”]).

Table 3: Total Sessions Attended by Condition

condition	mean_sessions	sd_sessions	n
Purrble Treatment	12.35526	2.237284	76
Waitlist Control	12.85714	2.056532	77

Attrition:

Results Text Attrition rates were low overall and did not differ significantly by condition, χ²(1, N = 153) = 0.11, p = .75, with 9.2% attrition in the Purrble condition (7 of 76 participants) and 6.5% attrition in the waitlist control condition (5 of 77 participants).

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

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

Results Text: “Across the full sample, regression analyses indicated a significant decline in participation over time, with the average number of weekly respondents decreasing by approximately 2.14 per week (SE = 0.29, t = –7.36, p < .001). When examined by condition, participation declined at a rate of –1.46 participants per week in the Purrble group (SE = 0.23, t = –6.22, p < .001) and –0.69 participants per week in the waitlist control (SE = 0.12, t = –5.82, p < .001). A time × condition interaction (β = 0.77, SE = 0.26, p = .007) suggested a steeper linear decline in the Purrble group, though the absolute difference was small.”

Across the full sample, participation declined by -2.16 per week (SE = 0.29, t = -7.39, p = 0.000).

Slope difference (Week × Condition) estimate = 0.76, SE = 0.26, t = 2.86, p = 0.009; 95% CI [0.21, 1.30]
Waitlist decline = -1.46 /week
Purrble decline  = -0.70 /week

Participation by Group Over Time

Reviewer’s Comment: “Report the response rate to weekly surveys over time. Declining engagement is common in mental health populations and raises risk of selective reporting.”

Response “We agree that reporting response rates over time is important to assess potential engagement decline and selective response bias. We have now included a table summarizing weekly participation rates by condition across the study period.”

Added Text, Results “Weekly response rates are summarized by condition in Table X and Figure X.”

Table: Weekly Participation Rates (% of Total Randomized) by Condition

Week	Purrble Treatment	Waitlist Control
1	97.4	94.8
2	97.4	96.1
3	98.7	96.1
4	94.7	90.9
5	89.5	92.2
6	88.2	92.2
7	89.5	93.5
8	90.8	94.8
9	80.3	87.0
10	82.9	85.7
11	81.6	85.7
12	65.8	87.0
13	81.6	88.3

Across the full sample, regression analyses indicated a significant decline in participation over time, with the average number of weekly respondents decreasing by approximately 2.14 per week (SE = 0.29, t = –7.36, p < .001). When examined by condition, participation declined at a rate of –1.46 participants per week in the Purrble group (SE = 0.23, t = –6.22, p < .001) and –0.70 participants per week in the waitlist control (SE = 0.12, t = –5.82, p < .001). A time × condition interaction (β = 0.77, SE = 0.26, p = .007) suggested a slightly steeper linear decline in the Purrble group, though the absolute difference was small (approximately 0.2–0.3 participants per week).

2.2. Preliminary Analyses

2.2.1 Descriptive Statistics

Reviewer Comment: “Please provide absolute group means and SDs at baseline and follow-up for all outcomes in the main text, not only adjusted differences.”

Response: “Thank you for pointing out this omission. We agree that presenting absolute group means and standard deviations provides important context for interpreting adjusted effects. We have now added a table summarizing pre- and post-test descriptive statistics (means and standard deviations) for all outcomes by condition.”

Added Text: Table X presents pre- and post-test descriptive statistics (means and standard deviations) for all primary and secondary outcomes by condition.

Means and standard deviations for each outcome by condition and time point

	Waitlist		Purrble
Outcome	Pre	Post	Pre	Post
Emotion Regulation	28.38 (4.32)	28.61 (6.52)	27.92 (5.10)	25.26 (7.80)
Anxiety	13.65 (3.74)	13.20 (4.46)	13.78 (4.25)	12.00 (5.47)
Depression	14.70 (4.24)	15.15 (5.93)	15.39 (4.90)	13.44 (6.66)

Means and standard deviations (M ± SD) for each outcome by condition, time point, and gender identity

Outcome	Identity Group	Condition	Pre	Post
Anxiety	Cisgender	Purrble	13.13 (4.11)	10.50 (5.37)
Anxiety	Cisgender	Waitlist	13.41 (3.45)	13.55 (4.57)
Anxiety	TGD	Purrble	14.46 (4.34)	13.46 (5.22)
Anxiety	TGD	Waitlist	13.88 (4.02)	12.85 (4.37)
Depression	Cisgender	Purrble	14.18 (4.67)	11.65 (6.84)
Depression	Cisgender	Waitlist	14.38 (4.32)	15.71 (6.54)
Depression	TGD	Purrble	16.66 (4.87)	15.18 (6.07)
Depression	TGD	Waitlist	15.00 (4.20)	14.59 (5.27)
Emotion Regulation	Cisgender	Purrble	27.31 (5.21)	23.03 (8.18)
Emotion Regulation	Cisgender	Waitlist	28.38 (4.13)	28.84 (6.97)
Emotion Regulation	TGD	Purrble	28.56 (4.97)	27.42 (6.85)
Emotion Regulation	TGD	Waitlist	28.38 (4.55)	28.38 (6.13)

2.2.2 Baseline Equivalence

Results Text: Baseline measures of outcome variables and participant age did not differ significantly between conditions.

### Table. Baseline Equivalence Across Conditions (Independent-Samples t-tests)

Variable	Dependent Variable	t	df	p	d	95% CI
Age	age	0.86	150.51	.392	0.14	[-0.18, 0.46]
Emotion Regulation (DERS-8)	Pre_DERS8_Sum	-0.60	146.06	.551	-0.10	[-0.41, 0.22]
Anxiety (GAD-7)	Pre_GAD7_Sum	0.20	147.61	.840	0.03	[-0.29, 0.35]
Depression (PHQ-9)	Pre_PHQ9_Sum	0.93	147.00	.353	0.15	[-0.17, 0.47]

##2.2.3 Outliers

Methods Text: Second, we performed multivariate outlier analyses to identify influential data points (63).

Results Text: We examined potential multivariate outliers among baseline variables (Pre-DERS8, Pre-GAD7, Pre-PHQ9) using Mahalanobis distance. Distances were compared to the χ² distribution with 3 degrees of freedom at p < .99 (critical value = 11.34). One participant exceeded this threshold (D² = 14.57), indicating a somewhat atypical combination of baseline emotion-regulation, anxiety, and depression scores. To evaluate influence on model results, we reran all primary analyses (ANCOVA and linear mixed-effects models) with and without this participant. The pattern, magnitude, and significance of results were unchanged. Accordingly, all analyses were reported using the full sample.

FALSE  TRUE 
  151     1 

Outlier participant(s) based on Mahalanobis distance (p < .99):

##2.2.4 Attrition Analysis. Methods Text: Third, we conducted attrition analyses (64), with attrition operationalised as participants failing to fill in any follow-up questionnaires (Weeks 11–13). A binary indicator was created to represent follow-up completion (1 = filled in at least one follow-up questionnaire; 0 = filled in none). Attrition rates were calculated overall, by condition, and by gender identity, using chi-square tests to determine whether attrition differed by condition or gender identity.

Results Text: Chi-square tests indicated that attrition rates did not differ significantly by condition, χ²(1) = 0.11, p = .75, or by gender identity, χ²(1) <0.01, p = 1. While and there were no main or interactive effects of attrition on outcomes.

### Chi-square test for attrition by Condition :

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

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

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

condition	n	Completed	Not_Completed	attrition_rate	attrition_percent
Purrble Treatment	76	69	7	0.0921053	9.2
Waitlist Control	77	72	5	0.0649351	6.5

NULL


### Chi-square test for attrition by Gender Identity :

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

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

Table: 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

NULL

Methods Text: Then, to assess potential attrition bias, we conducted two-way ANOVAs testing for Condition × Attrition Status effects on each baseline outcome variable.

Results Text: No main or interactive effects of attrition status were observed on any baseline variable, indicating no evidence of differential attrition

Table: Two-way ANOVAs for Baseline Outcomes by Condition and Attrition Status

Variable	Effect	df	F	p
Emotion Regulation (DERS-8)	Condition	1	0.356	0.552
Emotion Regulation (DERS-8)	Attrition Status	1	1.356	0.246
Emotion Regulation (DERS-8)	Condition × Attrition	1	0.114	0.736
Anxiety (GAD-7)	Condition	1	0.041	0.841
Anxiety (GAD-7)	Attrition Status	1	0.073	0.787
Anxiety (GAD-7)	Condition × Attrition	1	0.000	0.994
Depression (PHQ-9)	Condition	1	0.859	0.356
Depression (PHQ-9)	Attrition Status	1	0.132	0.717
Depression (PHQ-9)	Condition × Attrition	1	0.198	0.657

#2.3 Program Effects

2.3.1 # Main Effects Analyses

These are the main results for the paper here.

condition_num levels:
[1] 0 1

identity_group levels:
[1] 0 1

Parameter Estimates for Post_DERS8_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-0.959	-11.072	9.155	5.114	-0.188	0.852	NA	NA	NA
condition_num	-3.039	-4.916	-1.162	0.949	-3.202	0.002	0.090	0.027	1
Pre_DERS8_Sum	0.921	0.723	1.119	0.100	9.214	0.000	0.395	0.293	1
identity_group	1.693	-0.258	3.643	0.986	1.716	0.088	0.019	0.000	1
age	0.127	-0.291	0.544	0.211	0.600	0.549	0.003	0.000	1

Parameter Estimates for Post_GAD7_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-2.720	-9.151	3.711	3.252	-0.837	0.404	NA	NA	NA
condition_num	-1.350	-2.660	-0.040	0.663	-2.037	0.044	0.024	0.000	1
Pre_GAD7_Sum	0.739	0.576	0.902	0.082	8.979	0.000	0.388	0.285	1
identity_group	0.750	-0.621	2.121	0.693	1.082	0.281	0.003	0.000	1
age	0.271	-0.020	0.562	0.147	1.839	0.068	0.024	0.000	1

Parameter Estimates for Post_PHQ9_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-5.618	-12.580	1.343	3.520	-1.596	0.113	NA	NA	NA
condition_num	-2.604	-4.018	-1.191	0.715	-3.644	0.000	0.043	0.005	1
Pre_PHQ9_Sum	1.002	0.849	1.155	0.077	12.961	0.000	0.559	0.471	1
identity_group	0.254	-1.222	1.731	0.746	0.341	0.734	0.000	0.000	1
age	0.295	-0.018	0.607	0.158	1.864	0.064	0.025	0.000	1

Outlier Check: Re-run without T42

Results Text: The pattern, magnitude, and significance of results were unchanged. Accordingly, all analyses were reported using the full sample.

Main effects with adjusted means put into one neat table

Additionally, runs results with outlier removed (psid-T42)

condition_num levels:
[1] 0 1

identity_group levels:
[1] 0 1

Parameter Estimates for Post_DERS8_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-1.019	-11.160	9.121	5.127	-0.199	0.843	NA	NA	NA
condition_num	-2.995	-4.882	-1.107	0.954	-3.138	0.002	0.084	0.024	1
Pre_DERS8_Sum	0.916	0.717	1.115	0.101	9.106	0.000	0.391	0.289	1
identity_group	1.657	-0.302	3.616	0.990	1.673	0.097	0.018	0.000	1
age	0.135	-0.284	0.554	0.212	0.639	0.524	0.003	0.000	1

Parameter Estimates for Post_GAD7_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-2.657	-9.160	3.845	3.288	-0.808	0.420	NA	NA	NA
condition_num	-1.359	-2.678	-0.039	0.667	-2.036	0.044	0.028	0.000	1
Pre_GAD7_Sum	0.736	0.570	0.903	0.084	8.753	0.000	0.378	0.275	1
identity_group	0.760	-0.622	2.143	0.699	1.088	0.279	0.003	0.000	1
age	0.270	-0.023	0.562	0.148	1.822	0.071	0.024	0.000	1

Parameter Estimates for Post_PHQ9_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-5.441	-12.481	1.598	3.559	-1.529	0.129	NA	NA	NA
condition_num	-2.624	-4.045	-1.202	0.719	-3.651	0.000	0.051	0.008	1
Pre_PHQ9_Sum	0.996	0.840	1.153	0.079	12.605	0.000	0.548	0.458	1
identity_group	0.282	-1.205	1.770	0.752	0.375	0.708	0.000	0.000	1
age	0.291	-0.023	0.605	0.159	1.830	0.069	0.024	0.000	1

Error in select(mutate(broom::tidy(model, conf.int = TRUE), across(where(is.numeric),  : 
  unused arguments (term, estimate, conf.low, conf.high, std.error, statistic, p.value)

Reviewer’s Comment: Report effect sizes with 95% CIs for adjusted mean differences, standardized mean differences

My Response to Comment:
We thank the reviewer for this helpful suggestion. We have now added both unstandardized and standardized effect sizes, each reported with their 95% confidence intervals. Specifically, we:

Computed adjusted mean differences (β) between the Purrble and waitlist control conditions using estimated marginal means from the ANCOVA models, along with their 95% CIs.

Calculated standardized mean differences (Cohen’s d) and corresponding 95% CIs using the emmeans::eff_size() function, based on the model residual variance.

Added these results in a new summary table following each ANCOVA table (see Table X).

This table now reports, for each outcome, the adjusted group means, adjusted mean difference with 95% CI, and standardized mean difference (Cohen’s d) with 95% CI, as requested.

Error in contrast.emmGrid(object, method, adjust = "none", ...) : 
  Contrast function 'cohen.emmc' not found

Error in select(effectsize::eta_squared(model, partial = TRUE), Parameter,  : 
  unused arguments (Parameter, Eta2_partial)

Robustness Check using the Benjamini–Hochberg (BH) False Discovery Rate (FDR) procedure.

This robustness check accounts for multiple statistical tests across the three primary outcomes by applying the Benjamini–Hochberg procedure, which controls the false discovery rate (FDR). This method is less conservative than Bonferroni and is appropriate when outcomes are conceptually related but not fully independent. All primary outcome effects remain statistically significant after correction (FDR q < .05), supporting the robustness of the main findings.

[1] 0.003 0.044 0.000

Reliable Change Indices

DERS-8

GAD-7

PHQ-9

How many showed reliable change on all 3 measures?

2.3.1 Moderation Analyses

condition_num levels:
[1] 0 1

identity_group levels:
[1] 0 1

Parameter Estimates for Post_DERS8_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	0.316	-9.746	10.378	5.087	0.062	0.951	NA	NA	NA
condition_num	-5.006	-7.629	-2.382	1.326	-3.774	0.000	0.092	0.029	1
Pre_DERS8_Sum	0.913	0.717	1.108	0.099	9.238	0.000	0.403	0.301	1
identity_group	-0.242	-2.897	2.412	1.342	-0.181	0.857	0.020	0.000	1
age	0.122	-0.290	0.534	0.208	0.587	0.558	0.003	0.000	1
condition_num:identity_group	3.924	0.220	7.628	1.873	2.095	0.038	0.032	0.001	1

Parameter Estimates for Post_GAD7_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-1.819	-8.214	4.577	3.234	-0.562	0.575	NA	NA	NA
condition_num	-2.777	-4.606	-0.948	0.925	-3.004	0.003	0.025	0.000	1
Pre_GAD7_Sum	0.728	0.567	0.889	0.081	8.946	0.000	0.396	0.294	1
identity_group	-0.651	-2.506	1.205	0.938	-0.694	0.489	0.003	0.000	1
age	0.268	-0.019	0.555	0.145	1.845	0.067	0.025	0.000	1
condition_num:identity_group	2.857	0.267	5.446	1.309	2.182	0.031	0.034	0.002	1

Parameter Estimates for Post_PHQ9_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-4.721	-11.697	2.255	3.527	-1.338	0.183	NA	NA	NA
condition_num	-3.864	-5.840	-1.888	0.999	-3.868	0.000	0.044	0.005	1
Pre_PHQ9_Sum	0.987	0.835	1.140	0.077	12.792	0.000	0.565	0.478	1
identity_group	-0.983	-2.987	1.021	1.013	-0.970	0.334	0.000	0.000	1
age	0.291	-0.019	0.601	0.157	1.858	0.065	0.026	0.000	1
condition_num:identity_group	2.543	-0.267	5.353	1.421	1.790	0.076	0.023	0.000	1

condition_num levels:
[1] 0 1

identity_group levels:
[1] 0 1

Parameter Estimates for Post_DERS8_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	0.316	-9.746	10.378	5.087	0.062	0.951	NA	NA	NA
condition_num	-5.006	-7.629	-2.382	1.326	-3.774	0.000	0.092	0.029	1
Pre_DERS8_Sum	0.913	0.717	1.108	0.099	9.238	0.000	0.403	0.301	1
identity_group	-0.242	-2.897	2.412	1.342	-0.181	0.857	0.020	0.000	1
age	0.122	-0.290	0.534	0.208	0.587	0.558	0.003	0.000	1
condition_num:identity_group	3.924	0.220	7.628	1.873	2.095	0.038	0.032	0.001	1

Parameter Estimates for Post_GAD7_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-1.819	-8.214	4.577	3.234	-0.562	0.575	NA	NA	NA
condition_num	-2.777	-4.606	-0.948	0.925	-3.004	0.003	0.025	0.000	1
Pre_GAD7_Sum	0.728	0.567	0.889	0.081	8.946	0.000	0.396	0.294	1
identity_group	-0.651	-2.506	1.205	0.938	-0.694	0.489	0.003	0.000	1
age	0.268	-0.019	0.555	0.145	1.845	0.067	0.025	0.000	1
condition_num:identity_group	2.857	0.267	5.446	1.309	2.182	0.031	0.034	0.002	1

Parameter Estimates for Post_PHQ9_Sum

Predictor	β	95% CI (Low)	95% CI (High)	SE	t	p	Partial η²	η² 95% CI (Low)	η² 95% CI (High)
(Intercept)	-4.721	-11.697	2.255	3.527	-1.338	0.183	NA	NA	NA
condition_num	-3.864	-5.840	-1.888	0.999	-3.868	0.000	0.044	0.005	1
Pre_PHQ9_Sum	0.987	0.835	1.140	0.077	12.792	0.000	0.565	0.478	1
identity_group	-0.983	-2.987	1.021	1.013	-0.970	0.334	0.000	0.000	1
age	0.291	-0.019	0.601	0.157	1.858	0.065	0.026	0.000	1
condition_num:identity_group	2.543	-0.267	5.353	1.421	1.790	0.076	0.023	0.000	1

Simple Slopes for DERS

JOHNSON-NEYMAN INTERVAL

When identity_group is OUTSIDE the interval [0.75, 14.45], the slope of condition_num is p < .05.

Note: The range of observed values of identity_group is [0.00, 1.00]

SIMPLE SLOPES ANALYSIS

Slope of condition_num when identity_group = 0.00 (0): 

   Est.   S.E.   t val.      p
------- ------ -------- ------
  -5.01   1.33    -3.77   0.00

Slope of condition_num when identity_group = 1.00 (1): 

   Est.   S.E.   t val.      p
------- ------ -------- ------
  -1.08   1.32    -0.82   0.42

 condition_num identity_group emmean    SE  df lower.CL upper.CL
             0              0   28.6 0.930 134     26.8     30.5
             1              0   23.6 0.963 134     21.7     25.5
             0              1   28.4 0.949 134     26.5     30.3
             1              1   27.3 0.942 134     25.4     29.2

Confidence level used: 0.95 

Simple Slopes for GAD

JOHNSON-NEYMAN INTERVAL

When identity_group is OUTSIDE the interval [0.52, 5.77], the slope of condition_num is p < .05.

Note: The range of observed values of identity_group is [0.00, 1.00]

SIMPLE SLOPES ANALYSIS

Slope of condition_num when identity_group = 0.00 (0): 

   Est.   S.E.   t val.      p
------- ------ -------- ------
  -2.78   0.92    -3.00   0.00

Slope of condition_num when identity_group = 1.00 (1): 

  Est.   S.E.   t val.      p
------ ------ -------- ------
  0.08   0.93     0.09   0.93

 condition_num identity_group emmean    SE  df lower.CL upper.CL
             0              0   13.6 0.650 134    12.31     14.9
             1              0   10.8 0.673 134     9.49     12.2
             0              1   12.9 0.662 134    11.64     14.3
             1              1   13.0 0.661 134    11.72     14.3

Confidence level used: 0.95 

Moderation analysis: Condition × Gender Identity (identity_group_num) interaction effects

Outcome	F	df	p	Beta_Int	95% CI (β)	η²ₚ	95% CI (η²ₚ)
Post_DERS8_Sum	4.39	1, 134	0.038	3.92	[0.22, 7.63]	0.032	[0.001, 1.000]
Post_GAD7_Sum	4.76	1, 134	0.031	2.86	[0.27, 5.45]	0.034	[0.002, 1.000]
Post_PHQ9_Sum	3.20	1, 134	0.076	2.54	[-0.27, 5.35]	0.023	[0.000, 1.000]

MAIN EFFECTS REVIEWER COMMENTS AND FOLLOW UP OUTLIER

“Provide sensitivity analyses to address possible bias from faster engagement decline in the intervention arm.”

[1] 0.057 0.057 0.076

Anova Table (Type III tests)

Response: Post_DERS8_Sum
                             Sum Sq Df F value   Pr(>F)   
condition_num:total_sessions 231.33  1  7.8344 0.005889 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Anova Table (Type III tests)

Response: Post_DERS8_Sum
                             Sum Sq Df F value   Pr(>F)   
condition_num:total_sessions 231.33  1  7.8344 0.005889 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
 condition_num total_sessions.trend    SE  df lower.CL upper.CL
             0                0.877 0.590 133   -0.289    2.043
             1               -1.077 0.374 133   -1.816   -0.338

Results are averaged over the levels of: identity_group_num 
Confidence level used: 0.95 

[1] "--- GAD-7 Interaction F-Test ---"
Anova Table (Type III tests)

Response: Post_GAD7_Sum
                             Sum Sq Df F value Pr(>F)
condition_num:total_sessions 7.9472  1  0.5176 0.4731
[1] "--- GAD-7 Simple Slopes ---"
 condition_num total_sessions.trend    SE  df lower.CL upper.CL
             0              -0.0155 0.425 133   -0.857    0.826
             1              -0.3825 0.277 133   -0.930    0.165

Results are averaged over the levels of: identity_group_num 
Confidence level used: 0.95 
[1] "--- PHQ-9 Interaction F-Test ---"
Anova Table (Type III tests)

Response: Post_PHQ9_Sum
                             Sum Sq Df F value Pr(>F)
condition_num:total_sessions 34.323  1  1.9442 0.1655
[1] "--- PHQ-9 Simple Slopes ---"
 condition_num total_sessions.trend    SE  df lower.CL upper.CL
             0                0.336 0.455 133   -0.565    1.237
             1               -0.424 0.297 133   -1.012    0.165

Results are averaged over the levels of: identity_group_num 
Confidence level used: 0.95 

Linear Mixed Effects Models

### Outcome: DERS8_Sum 

Mixed-Effects Model for DERS8_Sum controlling for identity_group and age

effect	group	term	estimate	std.error	statistic	df	p.value
fixed	NA	(Intercept)	22.585	3.556	6.352	148.090	0.000
fixed	NA	Week	-0.123	0.045	-2.729	148.679	0.007
fixed	NA	condition1	0.051	0.414	0.122	148.816	0.903
fixed	NA	identity_group1	-0.465	0.412	-1.128	148.226	0.261
fixed	NA	age	0.277	0.174	1.586	147.702	0.115
fixed	NA	Week:condition1	-0.142	0.045	-3.137	148.680	0.002
ran_pars	psid	sd__(Intercept)	4.592	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.102	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.468	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.609	NA	NA	NA	NA

### Outcome: GAD7_Sum 

Mixed-Effects Model for GAD7_Sum controlling for identity_group and age

effect	group	term	estimate	std.error	statistic	df	p.value
fixed	NA	(Intercept)	11.475	2.753	4.168	148.984	0.000
fixed	NA	Week	-0.106	0.032	-3.324	149.152	0.001
fixed	NA	condition1	0.028	0.340	0.081	149.340	0.936
fixed	NA	identity_group1	-0.625	0.319	-1.961	148.747	0.052
fixed	NA	age	0.111	0.135	0.820	148.215	0.414
fixed	NA	Week:condition1	-0.050	0.032	-1.568	149.150	0.119
ran_pars	psid	sd__(Intercept)	3.695	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.234	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.292	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.220	NA	NA	NA	NA

### Outcome: PHQ9_Sum 

Mixed-Effects Model for PHQ9_Sum controlling for identity_group and age

effect	group	term	estimate	std.error	statistic	df	p.value
fixed	NA	(Intercept)	14.374	3.298	4.358	148.057	0.000
fixed	NA	Week	-0.067	0.033	-2.020	148.491	0.045
fixed	NA	condition1	0.604	0.377	1.603	148.673	0.111
fixed	NA	identity_group1	-0.816	0.382	-2.135	148.272	0.034
fixed	NA	age	0.037	0.162	0.227	147.820	0.821
fixed	NA	Week:condition1	-0.110	0.033	-3.287	148.491	0.001
ran_pars	psid	sd__(Intercept)	4.186	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	0.058	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.312	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.262	NA	NA	NA	NA

NA

###Reviewer Comment: Sensitivity Analysis

Reviewer Comment: “Provide sensitivity analyses to address possible bias from faster engagement decline in the intervention arm.”

My Response to Comment: Because engagement analyses demonstrated a faster rate of decline in the Purrble arm compared to the waitlist control, we conducted sensitivity analyses to examine whether the total number of sessions completed by each participant was associated with intervention outcomes. The number of sessions participated was added as a covariate in all ANCOVA models. Across outcomes, inclusion of this covariate did not alter the pattern, magnitude, or significance of results, and number of sessions was not a significant predictor in any model. These findings indicate that differences in the rate of survey responsiveness did not bias the primary results.

Reviewer Comment: “Include sensitivity analyses addressing differential engagement between arms.”

My Response to Comment: To further examine potential differences in engagement between study arms, we compared the total number of sessions completed across conditions and included this variable as a covariate in all outcome models. Although participants in the Purrble arm completed slightly fewer sessions on average than those in the waitlist condition, this difference did not affect any outcome. Results remained consistent with primary analyses, suggesting that differential engagement between arms did not account for the observed intervention effects.

Results Text: Because engagement analyses indicated a faster rate of decline in the Purrble arm compared to the waitlist control, we conducted sensitivity analyses to examine whether the total number of sessions completed by each participant was associated with intervention outcomes. The number of sessions participated was added as a covariate in all models. Across outcomes, inclusion of this covariate did not alter the pattern, magnitude, or significance of results, and number of sessions was not a significant predictor in any model.

### Sensitivity ANCOVA (including total_sessions) for Post_DERS8_Sum 

ANCOVA (Type III) results including all covariates for Post_DERS8_Sum

Source	df	F	p	η²ₚ	95% CI (η²ₚ)
(Intercept)	1	0.12	0.730	NA	NA
condition	1	12.00	0.001	0.091	[0.028, 1.000]
Pre_DERS8_Sum	1	83.59	0.000	0.400	[0.298, 1.000]
identity_group_num	1	3.58	0.061	0.019	[0.000, 1.000]
age	1	0.44	0.507	0.003	[0.000, 1.000]
total_sessions	1	2.55	0.112	0.019	[0.000, 1.000]
Residuals	134	NA	NA	NA	NA

**Adjusted Means (Condition Only)**

Outcome	AdjMean_WL	AdjMean_PB
Post_DERS8_Sum	28.65	25.32

### Sensitivity ANCOVA (including total_sessions) for Post_GAD7_Sum 

ANCOVA (Type III) results including all covariates for Post_GAD7_Sum

Source	df	F	p	η²ₚ	95% CI (η²ₚ)
(Intercept)	1	0.02	0.885	NA	NA
condition	1	4.95	0.028	0.025	[0.000, 1.000]
Pre_GAD7_Sum	1	74.54	0.000	0.390	[0.288, 1.000]
identity_group_num	1	1.51	0.222	0.003	[0.000, 1.000]
age	1	3.58	0.060	0.025	[0.000, 1.000]
total_sessions	1	1.40	0.239	0.010	[0.000, 1.000]
Residuals	134	NA	NA	NA	NA

**Adjusted Means (Condition Only)**

Outcome	AdjMean_WL	AdjMean_PB
Post_GAD7_Sum	13.36	11.86

### Sensitivity ANCOVA (including total_sessions) for Post_PHQ9_Sum 

ANCOVA (Type III) results including all covariates for Post_PHQ9_Sum

Source	df	F	p	η²ₚ	95% CI (η²ₚ)
(Intercept)	1	0.86	0.356	NA	NA
condition	1	13.84	0.000	0.044	[0.005, 1.000]
Pre_PHQ9_Sum	1	156.31	0.000	0.561	[0.472, 1.000]
identity_group_num	1	0.20	0.658	0.000	[0.000, 1.000]
age	1	3.57	0.061	0.025	[0.000, 1.000]
total_sessions	1	0.62	0.433	0.005	[0.000, 1.000]
Residuals	134	NA	NA	NA	NA

**Adjusted Means (Condition Only)**

Outcome	AdjMean_WL	AdjMean_PB
Post_PHQ9_Sum	15.67	12.96

Anova Table (Type III tests)

Response: Post_DERS8_Sum
                             Sum Sq Df F value   Pr(>F)   
condition_num:total_sessions 231.33  1  7.8344 0.005889 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Anova Table (Type III tests)

Response: Post_DERS8_Sum
                             Sum Sq Df F value   Pr(>F)   
condition_num:total_sessions 231.33  1  7.8344 0.005889 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 condition_num total_sessions.trend    SE  df lower.CL upper.CL
             0                0.877 0.590 133   -0.289    2.043
             1               -1.077 0.374 133   -1.816   -0.338

Results are averaged over the levels of: identity_group_num 
Confidence level used: 0.95 

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.

Number of Responses for Self-Harm Questions Over Time
Week	N_SHQ1	N_SHQ2	N_SHQ3
1	146	146	146
2	148	148	148
3	149	149	149
4	141	141	141
5	139	139	139
6	138	138	138
7	140	140	140
8	141	141	141
9	127	127	127
10	128	128	128
11	128	128	128
12	117	117	117
13	130	130	130

library(dplyr) library(tidyr) library(ggplot2) library(gt)

Reshape into long format

shq_long <- NoDup_PurrbleAnon %>% select(Week, SHQ1, SHQ2, SHQ3) %>% pivot_longer(cols = starts_with(“SHQ”), names_to = “SHQ_Var”, values_to = “Response”) %>% filter(!is.na(Week) & Week != 0) %>% filter(!is.na(Response)) %>% mutate(Response = factor(Response, levels = c(1, 0), labels = c(“1”, “0”)))

Count how many selected each category (0 or 1) per SHQ variable per week

shq_counts <- shq_long %>% group_by(Week, SHQ_Var, Response) %>% summarise(n = n(), .groups = “drop”)

#———————————————————- # Plot: Line Graph of 1 (flagged) response over time #———————————————————- ggplot( shq_counts %>% filter(Response == “1”), aes(x = Week, y = n, color = SHQ_Var) ) + geom_line(size = 1) + labs( title = “Number of Flagged SHQ Responses Over Time (Response = 1)”, x = “Week”, y = “Count of Response = 1”, color = “SHQ Variable” ) + theme_minimal() + scale_x_continuous(breaks = unique(shq_counts$Week))

#———————————————————- # Table: Count of 0 and 1 Responses per Week per SHQ #———————————————————- shq_counts %>% pivot_wider(names_from = Response, values_from = n, values_fill = 0) %>% rename(Response = 1 = 1, Response = 0 = 0) %>% gt() %>% tab_header(title = “Counts of SHQ Responses (0 vs. 1) by Week and Variable”)

Reshape into long format and include condition

shq_long_grouped <- NoDup_PurrbleAnon %>% select(psid, Week, condition, SHQ1, SHQ2, SHQ3) %>% pivot_longer(cols = starts_with(“SHQ”), names_to = “SHQ_Var”, values_to = “Response”) %>% filter(!is.na(Week) & Week != 0) %>% filter(!is.na(Response)) %>% mutate(Response = factor(Response, levels = c(1, 0), labels = c(“1”, “0”)), condition = as.factor(condition))

Count how many selected each category (0 or 1) per SHQ variable, per week, per group

shq_counts_grouped <- shq_long_grouped %>% group_by(Week, condition, SHQ_Var, Response) %>% summarise(n = n(), .groups = “drop”)

#———————————————————- # Plot: Line Graph of 1 (flagged) response over time by group #———————————————————- ggplot( shq_counts_grouped %>% filter(Response == “1”), aes(x = Week, y = n, color = SHQ_Var) ) + geom_line(size = 1) + facet_wrap(~ condition) + labs( title = “Number of Flagged SHQ Responses Over Time (Response = 1)”, subtitle = “Faceted by Condition”, x = “Week”, y = “Count of Response = 1”, color = “SHQ Variable” ) + theme_minimal() + scale_x_continuous(breaks = unique(shq_counts_grouped$Week))

#———————————————————- # Table: Count of 0 and 1 Responses per Week per SHQ, by Group #———————————————————- shq_counts_grouped %>% pivot_wider(names_from = Response, values_from = n, values_fill = 0) %>% rename(Response = 1 = 1, Response = 0 = 0) %>% arrange(condition, SHQ_Var, Week) %>% gt() %>% tab_header(title = “Counts of SHQ Responses (0 vs. 1) by Week, Variable, and Group”)

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	1.07	0.226	0.99	0.206	0.93	0.273	1.05	0.217
Waitlist Control	—	—	—	—	—	—	—	—
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	0.045	0.182	1.046	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	1.367	1.918	3.922	0.713	0.476
Screener 1	2|3	2.455	1.930	11.647	1.272	0.203
Screener 1	3|4	4.890	1.980	132.932	2.469	0.014
Screener 2	condition1	0.150	0.214	1.162	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	24.860	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	3.849	2.227	46.955	1.728	0.084
Screener 2	2|3	5.360	2.263	212.790	2.369	0.018
Screener 2	3|4	7.300	2.324	1479.978	3.141	0.002
Screener 3	condition1	0.049	0.275	1.050	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	1.357	2.828	3.886	0.480	0.631
Screener 3	2|3	2.649	2.850	14.133	0.929	0.353

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)	22.585	3.556	6.352	148.090	0.000	15.616	29.555
fixed	NA	Week	-0.123	0.045	-2.729	148.679	0.007	-0.212	-0.035
fixed	NA	condition1	0.051	0.414	0.122	148.816	0.903	-0.761	0.862
fixed	NA	identity_group1	-0.465	0.412	-1.128	148.226	0.261	-1.272	0.343
fixed	NA	age	0.277	0.174	1.586	147.702	0.115	-0.065	0.618
fixed	NA	Week:condition1	-0.142	0.045	-3.137	148.680	0.002	-0.230	-0.053
ran_pars	psid	sd__(Intercept)	4.592	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.102	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.609	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)	22.585	3.556	6.352	148.090	0.000	15.616	29.555
fixed	NA	Week	-0.123	0.045	-2.729	148.679	0.007	-0.212	-0.035
fixed	NA	condition1	0.051	0.414	0.122	148.816	0.903	-0.761	0.862
fixed	NA	identity_group1	-0.465	0.412	-1.128	148.226	0.261	-1.272	0.343
fixed	NA	age	0.277	0.174	1.586	147.702	0.115	-0.065	0.618
fixed	NA	Week:condition1	-0.142	0.045	-3.137	148.680	0.002	-0.230	-0.053
ran_pars	psid	sd__(Intercept)	4.592	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.102	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.468	NA	NA	NA	NA	NA	NA
ran_pars	Residual	sd__Observation	3.609	NA	NA	NA	NA	NA	NA

# R2 for Mixed Models

  Conditional R2: 0.717
     Marginal R2: 0.037

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)	11.475	2.753	4.168	148.984	0.000	6.079	16.871
fixed	NA	Week	-0.106	0.032	-3.324	149.152	0.001	-0.169	-0.044
fixed	NA	condition1	0.028	0.340	0.081	149.340	0.936	-0.639	0.694
fixed	NA	identity_group1	-0.625	0.319	-1.961	148.747	0.052	-1.249	0.000
fixed	NA	age	0.111	0.135	0.820	148.215	0.414	-0.154	0.375
fixed	NA	Week:condition1	-0.050	0.032	-1.568	149.150	0.119	-0.113	0.013
ran_pars	psid	sd__(Intercept)	3.695	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	-0.234	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.292	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)	14.374	3.298	4.358	148.057	0.000	7.909	20.839
fixed	NA	Week	-0.067	0.033	-2.020	148.491	0.045	-0.133	-0.002
fixed	NA	condition1	0.604	0.377	1.603	148.673	0.111	-0.135	1.342
fixed	NA	identity_group1	-0.816	0.382	-2.135	148.272	0.034	-1.564	-0.067
fixed	NA	age	0.037	0.162	0.227	147.820	0.821	-0.280	0.354
fixed	NA	Week:condition1	-0.110	0.033	-3.287	148.491	0.001	-0.175	-0.044
ran_pars	psid	sd__(Intercept)	4.186	NA	NA	NA	NA	NA	NA
ran_pars	psid	cor__(Intercept).Week	0.058	NA	NA	NA	NA	NA	NA
ran_pars	psid	sd__Week	0.312	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

New Analyses: Engagement

TWEETS

Methods Text: Perceived engagement with the intervention was assessed weekly using an averaged composite measure (Tweets_Avg) that reflected how well participants felt the intervention fit their needs and goals. To examine changes in engagement quality over time, we fit a linear mixed-effects model using restricted maximum likelihood (REML). Week was included as a fixed effect to model linear change, and participant ID (psid) was included as a random intercept to account for individual differences in baseline engagement perceptions. This model structure allowed us to estimate overall trajectories of perceived engagement while accommodating repeated measures within participants. Analyses were conducted in R using the lme4 and lmerTest packages, with degrees of freedom estimated using Satterthwaite’s method.

Results Text: The linear mixed-effects model revealed a significant decline in perceived engagement across the intervention period (b = −0.04, SE = 0.006, t(531) = −6.61, p < .001).

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Tweets_Avg ~ Week + (1 | psid)
   Data: .

REML criterion at convergence: 924.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.3610 -0.4855  0.0114  0.5652  3.1417 

Random effects:
 Groups   Name        Variance Std.Dev.
 psid     (Intercept) 0.5854   0.7651  
 Residual             0.1732   0.4162  
Number of obs: 609, groups:  psid, 80

Fixed effects:
              Estimate Std. Error         df t value Pr(>|t|)    
(Intercept)   2.946915   0.101432 131.706233  29.053  < 2e-16 ***
Week         -0.039363   0.005956 531.473885  -6.609 9.44e-11 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
     (Intr)
Week -0.499

Moderation of Gender Identity with TWEETS

Results Text: To explore whether perceived engagement trajectories differed by gender identity, we extended the linear mixed-effects model to include gender identity (TGD vs. cisgender) and its interaction with Week. This allowed us to test both baseline differences in perceived fit and differences in the rate of change over time. There were no significant differences in initial perceptions of intervention fit by gender identity (b = −0.06, SE = 0.10, t(130) = −0.62, p = .54). However, a significant Week × Gender Identity interaction emerged (b = 0.017, SE = 0.006, t(531) = 2.93, p = .0035). Simple slopes indicated that both groups experienced a decline in engagement over time, but the decline was steeper among TGD participants (b = −0.056, 95% CI [−0.073, −0.040]) than among cisgender participants (b = −0.022, 95% CI [−0.038, −0.005]).

Linear mixed model fit by REML. t-tests use Satterthwaite's method [
lmerModLmerTest]
Formula: Tweets_Avg ~ Week * identity_group + (1 | psid)
   Data: tweets_pb

REML criterion at convergence: 926.1

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-5.3002 -0.5019  0.0319  0.5610  3.0953 

Random effects:
 Groups   Name        Variance Std.Dev.
 psid     (Intercept) 0.5768   0.7595  
 Residual             0.1712   0.4137  
Number of obs: 609, groups:  psid, 80

Fixed effects:
                       Estimate Std. Error         df t value
(Intercept)            2.950072   0.100764 130.455090  29.277
Week                  -0.038963   0.005922 530.719720  -6.579
identity_group1       -0.062469   0.100764 130.455090  -0.620
Week:identity_group1   0.017363   0.005922 530.719720   2.932
                     Pr(>|t|)    
(Intercept)           < 2e-16 ***
Week                 1.14e-10 ***
identity_group1       0.53637    
Week:identity_group1  0.00352 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Correlation of Fixed Effects:
            (Intr) Week   idnt_1
Week        -0.499              
idntty_grp1  0.024  0.001       
Wk:dntty_g1  0.001  0.019 -0.499

$emtrends
 identity_group Week.trend      SE  df lower.CL upper.CL
 C                 -0.0216 0.00846 532  -0.0382 -0.00499
 TGD               -0.0563 0.00830 534  -0.0726 -0.04003

Degrees-of-freedom method: kenward-roger 
Confidence level used: 0.95 

$contrasts
 contrast estimate     SE  df t.ratio p.value
 C - TGD    0.0347 0.0118 533   2.931  0.0035

Degrees-of-freedom method: kenward-roger