PR_quant_long.Rmd

---
title: Temporal exploration of the Interpersonal Theory of Suicide among adolescents
  during treatment
author:
- name: Atanas Janackovski
  affiliation: University of Wollongong
  email: aj347@uowmail.edu.au
- name: Frank P. Deane
  affiliation: University of Wollongong
  email: fdeane@uow.edu.au
- name: Alex Hains
  affiliation: University of Wollongong
  email: alex@1234.com
- name: Peter J. Kelly
  affiliation: University of Wollongong
  email: pkelly@uow.edu.au
date: "`r format(Sys.Date(), '%d %B, %Y')`"
bibliography: ./bib/MyLib.bib
biblio-style: biblatex-apa
csl: ./bib/apa.csl
link-citations: yes
colorlinks: yes
always_allow_html: true
---

```{r, cleanup, include = FALSE, results = "hide", warning = FALSE}
library("here")
rm(list = ls(all = TRUE))
source("./code/func.R")
source("./code/load.R")

list2env(readRDS("./data/proc/riclpm_df.rds"), .GlobalEnv)

opts_chunk$set(
  echo = FALSE,
  message = FALSE,
  warning = FALSE,
  results = "hide"
)

options(
  knitr.kable.NA = "",
  kableExtra.auto_format = FALSE,
  knitr.table.format =
    ifelse(knitr::pandoc_to("docx"), "simple",
      ifelse(knitr::pandoc_to("html"), "html", "latex")
    ),
  tinytex.verbose = TRUE
)
```

# Introduction

For every suicide there are many more people who attempt suicide.
In 15--29-year-olds, it is the fourth leading cause of death globally
[World Health Organization [WHO], -@WHO2021].
In Australia, it is the number one cause of death in young people with rates
continuing to rise [Australian Bureau of Statistics [ABS], -@abs2021].
The interpersonal theory of suicide (ITS) is an ideation-to-action
framework that proposes the underlying mechanisms of suicidal behaviours
[@joiner2005; @vanorden2010].
It posits that three state-type and one trait-type factor contribute to suicide.
The combination of the state-type factors: (1) perceived burdensomeness (that
you are a liability on others), (2) thwarted belongingness (lack of reciprocally
caring relationships), and (3) hopelessness (that burdensomeness and belonging
will not improve), are theorised to lead to suicidal desire.
The ITS states that the more severe that these perceptions and associated
thoughts are, the more severe the suicidal desire.
The fourth factor, acquired capability, is proposed to be more stable and may be
influenced by previous painful experiences (e.g., abuse, self-injury, contact
sports).
This fourth factor contributes to whether someone has the capability to make a
suicide attempt.
However, according to the theory, capability is not a risk in and of itself.
Without a desire for suicide---moderated by the intensity of perceptions of
burdensomeness, belongingness, and hopelessness---capability alone is not enough
to lead to a suicide attempt.
More specifically, the ITS states that the causal processes of suicidal desire
are a result of these other factors [@joiner2005; @vanorden2010].
As such, the theory asserts it can provide a "map and compass" [@joiner2009, p.
196] for assessment and intervention with suicidal people, and proposes
burdensomeness and belongingness be the targets of therapy [@joiner2009].


Assessing the putative causal processes specified by the ITS could help improve
treatment for young people at risk of suicide.
When conducting treatment and process oriented research, a number of
recommendations have been made to help strengthen the design and validity of
findings.
Specifically, when evaluating potential causal processes and testing the
dynamic interplay of theorised variables, there is a need to disaggregate the
between- and within-person differences [@hamaker2015; @cole2009].
Omitting idiographic factors inherently disconnects statistical models from the
theoretical models they seek to test, and potentially undermines the validity of
the empirical inferences [@curran2014; @hamaker2015; @hofmann2019a].
Likewise, single timepoint assessment is a potential impediment.
Causal psychological factors are often time-varying in nature, therefore
relationships between variables are best analysed longitudinally [@kraemer1997],
and ideally should include multiple waves of data (three or more) with shorter
intervals between lags [@cole2009; @hamaker2015].
Research utilising designs with the above features may offer improved
insights into the underlying causal processes and subsequently be more useful
in developing interventions [@hamaker2015; @cole2009].


Findings of ITS research, both in young people and in older populations,
generally indicate partial support for the theory's propositions [@chu2017;
@ma2016].
However, most of the extant studies use non-clinical populations and
cross-sectional designs.
Of the prospective research to date, the majority report only two timepoints
[@chu2017; @ma2016].
Whilst the body of longitudinal research that is more consistent with the design
principles outlined above is growing [e.g., @kleiman2017; @rogers2019;
@kyron2018], studies testing the theory with clinical populations of young
people are limited [@abbott2021; @czyz2019a; @zhang2021; @wu2020].
@czyz2019a conducted one of the most fine-grained assessments of the ITS to
date.
This study used ecological momentary assessment in a population of adolescents
(13--17-years-old, *N* = 34) admitted to hospital following a suicide attempt
and/or suicidal ideation.
Daily severity of thwarted belongingness, perceived burdensomeness,
hopelessness, and suicidal ideation was assessed for one month post-discharge.
The study reported that suicidal ideation auto-regressively predicted suicidal
ideation, whilst no cross-lagged relationships predicted suicidal ideation.
However, the interaction between thwarted belongingness and either
burdensomeness or hopelessness predicted same day and next day suicidal
ideation [@czyz2019a].
Two secondary analyses using data from a randomised control trial of cognitive
therapy for suicide prevention with homeless youth (18--24-years-old, *N* =
142--150) have also tested the ITS longitudinally [@zhang2021; @wu2020;
@slesnick2020].
One used a mediation path model with post treatment scores, tested whether
thwarted belongingness and perceived burdensomeness at 6-months mediated the
effects of social problem-solving at 3-months on suicidal ideation at 9-months
post treatment [@zhang2021].
The study found only perceived burdensomeness was a significant mediator
[@zhang2021].
The second study used a cross-lagged panel model to test associations between
thwarted belongingness, perceived burdensomeness and suicidal ideation at
baseline, 3-, 6-, and 9-months post treatment [@wu2020].
They reported that perceived burdensomeness at baseline predicted suicidal
ideation at 3-months, and suicidal ideation at 6-months predicted lower
perceived burdensomeness and thwarted belongingness at 9-months post treatment
[@wu2020].


@abbott2021 used a random-intercept cross-lagged panel model (RI-CLPM) to test
the effects of perceived burdensomeness and thwarted belongingness on suicidal
ideation with a treatment seeking sample of adolescents (12--18-years-old) at
baseline, midway, and completion of treatment of a 16-week intervention.
They found partial support for the propositions of the ITS, with burdensomeness
predicting suicidal ideation at baseline to midway, and suicidal ideation
predicting burdensomeness at midway to treatment completion.
Whilst these studies have certainly added to our understanding of the
processes underlying the ITS, there are a number of limitations.
All studies used small sample sizes (*N* = 34--150) [@abbott2021; @czyz2019a;
@wu2020; @zhang2021], only one study included hopelessness as a time-varying
predictor [@czyz2019a], and only two studies disaggregated the between-person
effects [@abbott2021; @czyz2019a].
Furthermore, three studies used time lags (2--6-months) [@abbott2021; @wu2020;
@zhang2021] which may not adequately capture the dynamic nature of the relations
between the time-varying factors proposed by the ITS [@cole2009; @hamaker2015;
@vanorden2010].
The ITS posits causal mechanisms that contribute to the development,
maintenance, and treatment of suicidal desire in individuals [@joiner2009;
@vanorden2010].
Given the general paucity of longitudinal research with the ITS and the
limitations to the studies outlined above, there is a need to further evaluate
how applicable the theory is in clinical populations of young people at risk of
suicide.


## Aims

This study aimed to evaluate the relationships between variables purported to be
important to the development and treatment of suicidal desire during treatment
using a naturalistic, longitudinal design.
We tested the associations between the factors proposed by the ITS: thwarted
belongingness, perceived burdensomeness, hopelessness and suicidal ideation over
the course of treatment.
To more accurately test the associations between the variables of interest, a
RI-CLPM was used to partial out the between-person variance such that the
relationships between study variables more accurately assessed the within-person
dynamic processes across time [@hamaker2015].
Additionally, given its correlation with suicide [American Psychiatric
Association [APA],-@americanpsychiatricassociation2013], depression was also
included in the model as a potential time-varying covariate.


# Method

We report how we determined our sample size, all data exclusions (if any), all
manipulations, and all measures in the study.
The present study was not preregistered.


## Participants

```{r, participant, include = TRUE, results = "hide", warning = FALSE}
p <-
  list(
    n = phd_fin_wide %>% group_by(sex),
    atsi = phd_fin_wide %>% group_by(atsi),
    cald = phd_fin_wide %>% group_by(cald)
  ) %>%
    map(~ .x %>%
      summarise(n = n()) %>%
      mutate(prc = sprintf("%.1f", n / sum(n) * 100)))

refs <-
  phd_fin %>%
  filter(
    session ==  1
    ## !is.na(c)
  ) %>%
  mutate(
    ref = case_when(
      referrer %in% c(1, 2) ~ "GP",
      referrer %in% 3       ~ "MH",
      referrer %in% 4       ~ "ED",
      referrer %in% 5       ~ "psychiatrist",
      referrer %in% 6       ~ "AHP",
      referrer %in% 7       ~ "oth_slf_fam_fr",
      referrer %in% 8       ~ "oth_slf_fam_fr",
      referrer %in% 9       ~ "oth_slf_fam_fr",
      TRUE                  ~ "miss"
    )
  ) %>%
  group_by(ref) %>%
  summarise(
    n = n()
  ) %>%
  mutate(
    prc = paste0(round(n / sum(n) * 100, 1), "%")
  ) %>%
  arrange(desc(n)) %>%
  adorn_totals()

```
The study was approved by the institutional Human Research Ethics Committee.
The dataset was a secondary analyses of data taken from a short-term outpatient
suicide prevention program located in the Illawarra Shoalhaven region of New
South Wales, Australia between
`r format(ymd(min(phd_fin$date)), "%B %d, %Y")` and
`r format(ymd(max(phd_fin$date)), "%B %d, %Y")`.
The service offered no fee psychological support for people aged 12--25 years
who were at mild to moderate risk of suicide and self-harm.
The final sample consisted of
`r paste0(n_distinct(phd_fin_wide$ID))` participants
(`r subset(p$n, sex %in% "female", prc)`% females,
`r subset(p$n, sex %in% "male", prc)`% male, and
`r subset(p$n, sex %in% "other", prc)`% non-binary).
There were
`r paste0(subset(p$atsi, atsi %in% "ATSI", n))`
participants in the total sample
(`r subset(p$atsi, atsi %in% "ATSI", prc)`%)
who identified as Aboriginal and/or Torres Strait Islander, and
`r paste0(subset(p$cald, cald %in% "yes", n))` participants
(`r subset(p$cald, cald %in% "yes", prc)`%)
who identified as having a culturally and linguistically diverse background.
The average age of the sample was
`r sprintf("%.2f", mean(phd_fin_wide$age, na.rm = TRUE))` years
(*SD* = `r sprintf("%.2f", sd(phd_fin_wide$age, na.rm = TRUE))`).
This was a naturalistic sample and duration of service engagement varied
depending on the clinical needs or recovery of the participants.
The average number of sessions attended in the current sample was
`r sprintf("%.2f", mean(phd_fin_wide$cov_sess, na.rm = TRUE))`,
(*SD* = `r sprintf("%.2f", sd(phd_fin_wide$cov_sess, na.rm = TRUE))`).
The majority of referrals were from primary care settings such as general
practitioners
(`r subset(refs, ref %in% "GP", prc)`)
public mental health services
(`r subset(refs, ref %in% "MH", prc)`)
or emergency departments
(`r subset(refs, ref %in% "ED", prc)`).
A further
`r subset(refs, ref %in% "AHP", prc)`
came from allied health professionals and
`r subset(refs, ref %in% "oth_slf_fam_fr", prc)`
from other referral sources including self, family and friends.
The remainder of participants
(`r subset(refs, ref %in% "miss", prc)`)
did not have source of referral information available.
Regarding the assessment of risk and suitability for services, participants'
overall level of risk was determined using a risk assessment matrix by a mental
health intake clinician or their treating clinician (psychologists or clinical
psychologists) at their initial session.
The risk assessment matrix rated risk as 'low', 'medium', or 'high', across a
number of potential issues, including mental state (e.g., depression,
psychosis), history of suicidal attempts or thoughts, substance misuse, client
strengths and availability of supports, client changeability of risk level, and
clinician's confidence in assessment information (e.g., gaps in/or conflicting
information, poor engagement).
Examples of risk ratings for suicidal ideation are: 'low' (nil or vague thoughts),
'moderate' (frequent thoughts; repeated threats); or 'high' (continual thoughts;
clear intention).
A cumulative risk score was tallied by summing the total number of 'low',
'medium', and 'high' ratings.
Clients deemed to be of lower or higher than mild to moderate risk were referred
to more appropriate services.
The treatment approach used was based on a cognitive behavioural therapy
framework tailored for suicide prevention [@stanley2009], although clinicians
were able to draw on different approaches in their clinical work.<!-- [@janackovski2021]. -->
All participants provided informed consent to have their clinical information
entered into a research databank, with parental/carer co-consent sought for
participants aged 12--14 years.
Not consenting to research participation did not change the treatment offered.


## Measures

*Interpersonal Needs Questionnaire (INQ)*.
The 15-item INQ [@vanorden2012] is a self-report measure designed specifically
to reflect the two interpersonal constructs of the ITS.
Items are rated on a 7-point Likert scale with higher scores indicating higher
severity.
Six items measure perceived burdensomeness (PB) and nine items measure thwarted
belongingness (TB).
The measure has been found to be a reliable and valid measure in adolescent
inpatient samples and young adults [@hill2014a; @horton2015].
Taking into account the multilevel nature of the data, we calculated overall,
between-level, and within-cluster
($\alpha$^*2l*^, $\alpha$^*b*^, and $\alpha$^*w*^ respectively)
composite reliability of the repeated measures [@lai2021].
The composite reliability for the current sample was
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$pb, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$pb, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$pb, label %in% "within", est)`)
for burdensomeness items, and
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$tb, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$tb, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$tb, label %in% "within", est)`)
for belongingness items.
The Intraclass Correlation Coefficient (ICC) was
`r meas_icc_fin$pb$iccp` (95% CI `r meas_icc_fin$pb$ci`) for PB,
indicating that about
`r meas_icc_fin$pb$bwp`
was due to between-person variability and about
`r meas_icc_fin$pb$wip`
was due to within-person fluctuations over time.
The ICC for TB was
`r meas_icc_fin$tb$iccp` (95% CI `r meas_icc_fin$tb$ci`),
indicating that about
`r meas_icc_fin$tb$wip`
was due to within-person fluctuations.


*Beck Hopelessness Scale (BHS)*.
Hopelessness was measured using the BHS [@beck1974].
However, the service changed from using the original 20 item true/false scale
[true = 1 and false = 0, @beck1974] to the short 4-item version during the data
collection period.
The latter included items 6, 7, 9, and 15 of the original, with a 6-point Likert
scale [@aish2001; @yip2006].
In order to use data from both versions of the BHS for analysis, the short-form
version had responses rescaled to 0--5, and then summed, providing scores that
fell into the same 0 to 20 range as the full-scale version.
In both cases, higher scores indicate higher severity.
Both versions have previously demonstrated strong internal reliability
[@beck1998].
The composite reliability was
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$bhs_20, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$bhs_20, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$bhs_20, label %in% "within", est)`)
 for the 20-item version, and
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$bhs_sf, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$bhs_sf, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$bhs_sf, label %in% "within", est)`)
for the 4-item version.
The ICC was
`r meas_icc_fin$pb$iccp` (95% CI `r meas_icc_fin$bhs_20$ci`) for 20-item version
indicating that about
`r meas_icc_fin$bhs_20$wip`
was due to within-person fluctuations.
The ICC for 4-item version was
`r meas_icc_fin$bhs_sf$iccp` (95% CI `r meas_icc_fin$bhs_sf$ci`),
indicating that about
`r meas_icc_fin$bhs_sf$wip`
was due to within-person fluctuations.


*Modified Scale for Suicidal Ideation (MSSI)*.
The MSSI [@miller1986] is a clinician-administered 18-item semi-structured
interview used to measure severity of suicidal ideation.
The first four questions are designed as screening items to identify those whose
suicidal ideation is severe enough to warrant administration of the entire scale
[@miller1986].[^4]
The MSSI has demonstrated high internal reliability in adult psychiatric
inpatient samples [@miller1986] and inpatient suicidal youth, with high
internal reliability on the total scores [$\alpha$ = .89, @pettit2009].
In the current sample the composite reliability of the MSSI was
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$si, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$si, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$si, label %in% "within", est)`).
The ICC for MSSI was
`r meas_icc_fin$si$iccp` (95% CI `r meas_icc_fin$si$ci`),
indicating that about
`r meas_icc_fin$si$wip`
was due to within-person fluctuations.


*Depression subscale of the Depression Anxiety and Stress Scale–short version
(DASS21-DEP)*.
The DASS21-DEP [@lovibond1995a] captures symptoms of depression.
Items are rated on a 4-point Likert scale and higher scores indicate higher
symptom severity.
Strong internal reliability has been demonstrated in non-clinical samples of
young people [@klonsky2009; @szabo2010], comparable to studies of adult clinical
and community samples [@antony1998].
Composite reliability of the DASS21-DEP in the current sample was
$\alpha$^*2l*^ =
`r subset(mcfa_alpha$dep, label %in% "overall", est)`
($\alpha$^*b*^ =
`r subset(mcfa_alpha$dep, label %in% "between", est)`,
$\alpha$^*w*^ =
`r subset(mcfa_alpha$dep, label %in% "within", est)`).
The ICC for DASS21-DEP was
`r meas_icc_fin$dep$iccp` (95% CI `r meas_icc_fin$dep$ci`),
indicating that about
`r meas_icc_fin$dep$wip`
was due to within-person fluctuations.


*Acquired Capability for Suicide Scale-Fearlessness About Death (ACSS-FAD)*.
The 7-item ACSS-FAD [@ribeiro2014; @vanorden2008] was used to assess capability
for suicide at baseline.
Items are rated on a 5-point Likert scale.
Higher scores indicate higher fearlessness about death [@vanorden2008].
Discriminant validity is evidenced by the non-significant relationship with
suicidal desire and depression [@vanorden2010].
The ACSS-FAD has demonstrated good internal consistency amongst clinical samples
of adolescents [@horton2015], and was $\alpha$ =
`r subset(meas_rel_fin, var == "ac", max)` in the current study.


*Inventory of Statements about Self-injury (ISAS)*.
The ISAS [@klonsky2009; @klonsky2008] was used to measure functions of
self-injurious behaviours at baseline.
It contains 39 items that measure intrapersonal and interpersonal functions of
self-injury.
Items are rated on a 3-point Likert scale.
Higher scores on these subscales indicate stronger endorsement of the functions
for the participant [@klonsky2009].
The ISAS has good test-retest reliability [@glenn2011] and construct validity
demonstrated in a clinical sample [@klonsky2015a].
Reliability for ISAS section 2 was $\alpha$ =
`r subset(meas_rel_fin, var == "interp", max)`
for interpersonal and
$\alpha$ =
`r subset(meas_rel_fin, var == "intrap", max)`
for intrapersonal subscales.


*Demographics*.
During participants' initial session, treating clinicians also collected data on
demographic and background clinical factors.
This included ethnicity, relationship status, living arrangements, as well as
previous history of deliberate self-injury, trauma, and suicide attempts.
The total number of intervention sessions each participant received was also
recorded.


## Plan of analysis

### Random Intercept Cross-Lagged Panel Model


All preparation and analysis of data was carried out using R [v4.1.1,
@rcoreteam2021].[^3]
A random intercept cross-lagged panel model [RI-CLPM, @hamaker2015; @mulder2021]
analysis using 'lavaan' [@rosseel2012] was performed to test the direction of
effects between ITS variables and suicidal ideation across five waves of data.
Model fit was assessed using the Comparative Fit Index (CFI), the Tucker-Lewis
Index (TFI) the Root Mean Square Error of Approximation (RMSEA), and the
Standardized Root Mean Square Residual (SRMR).
Whilst a significant chi-square statistic indicates poor fit, this test is
sensitive to large sample size and may reject the null hypothesis (suggesting
poor fit) when other indicators suggest otherwise.
Alternatively, RMSEA and SRMR values < .05, and CFI and TLI values > .95 would
be considered a good fit of the model to the data [@hu1999].


The traditional cross-lagged panel model (CLPM) allows individuals to vary
across the group means and does not estimate between-person differences.
However, it is rarely the case that there is no between-person variation in
traits, which can result in biased and inaccurate estimates of regression
coefficients [@hamaker2015].
The RI-CLPM addresses this limitation through distinguishing the between-person
(time-invariant or trait-like) and within-person (time-variant or state-like)
variance by creating one latent variable for each construct across the
measurement timepoints, with factor loadings constrained to 1 [@hamaker2015;
@mulder2021].
Constraining factor loadings in this way assumes that the random intercepts
have the exact same influence on the observed variables at each occasion
[@mulder2021].[^1]
These new random-intercept latent variables are added to the traditional CLPM
measure.
The correlations between these latent factors represent the relationship between
these trait-like portions of the variance.
After accounting for the trait-like component, interpretations of regression
coefficients are then relative to each individual’s own mean or state variations
in the constructs.
The state-like effect was modelled by regressing each observed variable onto its
own latent factor, and constraining its measurement error variances to zero.

Autoregressive paths in RI-CLPM models reflect within-person carryover from one
time period to the next, or the extent to which one’s later scores are predicted
by earlier states on the same construct.
The cross-lagged paths reflect the degree to which participants’ states on one
variable can be predicted by prior states on another variable, controlling for
other variables in the model.
Across autoregressive and cross-lagged paths, a significant positive (negative)
relationship implies it will likely be followed by a positive (negative)
deviation in the expected score of the relevant construct at the next occasion
in the same direction.
Within-person correlations indicate cross-sectional correlations between
participants’ states on one variable and their states in another variable at the
same timepoint.
The assumption is that the within-person components at the first occasion are
not correlated to the random intercepts because observations have started at an
arbitrary timepoint in an ongoing process [@mulder2021].
Therefore, covariances between the within-person components at the first
occasion and the random intercepts are not included.
The CLPM is a special case of the RI-CLPM and is nested within it, so we
performed a chi-square difference test to compare the fit of the RI-CLPM with
the traditional CLPM.
This comparison tests whether removing the random intercepts significantly
deteriorates model fit [@hamaker2015; @mulder2021].
Figure \@ref(fig:riclpm-mod) illustrates a full RI-CLPM using two of our five
variables for the sake of visual simplicity.

### Missing Data


Missing data was managed at the scale level and the model level.
Initially, for all continuous measures other than the MSSI, where there was 20%
or less missing items for a scale, the scale was prorated to calculate a
variable score, otherwise a participant's scores were considered missing on that
variable.
For the MSSI, given that data was missing for participants that did not warrant
the full administration of the measure, but to respect the potential missing
data not related to this administration procedure, manual imputation was carried
out to be able to compare participants on a uniform scale.
If the screening items were below the cutoff (indicating administration of
subsequent items should cease) then the remaining items 5 to 18 were scored 0.
If more than one of the screening items was missing, then the case was treated
as having missing data on the MSSI.
Regarding missingness at the model level (across waves), given data was
collected in a naturalistic treatment setting, missing data was expected, as
participants attended different numbers of sessions.
Full information maximum likelihood (FIML) estimation with robust standard
errors is one of the recommended approaches to handling missing data of this
kind, even data with nonnormal distributions [@rosseel2012; @yuan2000;
@muthen2011].
However, one assumption of the FIML approach is that data are missing at random
(MAR).
Data can be considered MAR when the missingness is related to some other
variable(s) in the data set, but not the missing variable itself [@enders2010].
To further improve the FIML approach, it is recommended that auxiliary variables
be included in the model.
This can help reduce bias, improve power, and provide more robust estimates.
The recommended method is the saturated correlates approach [@graham2003;
@enders2008; @enders2010; @blozis2013], which was implemented by the 'semTools' package
[@jorgensen2021].
Therefore a number of potential baseline correlates as well as variables related
to engagement in services were included as auxiliary variables.
Auxiliary variables consisted of participants' age, gender, personal history of
trauma, deliberate self-injury and suicide attempts, as well as baseline scores
on acquired capability and functions of deliberate self-injury.
Additionally, to take into account the variability of participants engagement in
treatment, the total number of sessions were included.


# Results

## Descriptive Analyses

Descriptive statistics, including means and standard deviations for session
frequency, total number of sessions, age at baseline, acquired capability, and
sample proportions of gender, personal history of trauma and deliberate
self-injury are presented in Table \@ref(tab:descr).
Mean and standard deviations, number observed and percentages missing compared
to time 1 for perceived burdensomeness, thwarted belongingness, hopelessness,
depression, and severity of suicidal ideation are presented in Table \@ref(tab:means).
Correlation between observed and auxiliary variables are presented
in the supplementary material.


## RI-CLPM Analyses

### Model Fit

The random-intercepts cross-lagged model (RI-CLPM) provided a good fit to the
data.[^2]
Results showed an adequate to good fit:
CFI = `r subset(fit_stat, stat == "cfi.robust", valpr)`,
TLI = `r subset(fit_stat, stat == "tli.robust", valpr)`,
RMSEA = `r subset(fit_stat, stat == "rmsea.robust", valpr)`
(95% CI [`r subset(fit_stat, stat == "rmsea.ci.lower.robust", valpr)`,
`r subset(fit_stat, stat == "rmsea.ci.upper.robust", valpr)`]),
SRMR = `r subset(fit_stat, stat == "srmr", valpr)`.
Furthermore, the RI-CLPM was compared to the traditional CLPM, which did not
include any random intercepts.
The CLPM was a significantly worse fit to the data,
($\Delta\chi^2$ =
`r subset(mod_diff, term == "clpm_fit", chisq_diff)`,
$\Delta$*df* = `r subset(mod_diff, term == "clpm_fit", df_diff)`,
 *p* `r subset(mod_diff, term == "clpm_fit", p_value)`),
suggesting that partitioning trait-like and state-like variance for random
intercepts was indicated.


### Correlation of Between and Within Person Factors

The correlation between the random intercepts is reported in Table
\@ref(tab:riclpm-cor).
Regarding the trait-like between-person variance portion of this model, we found
that the burdensomeness, belongingness, hopelessness, and depression random
intercepts all had significant variance with each other, *r*s =
`r subset(ri_cor$no, std.all %in% min(std.all), r)` to
`r subset(ri_cor$no, std.all %in% max(std.all), r)`,
*p*s `r subset(ri_cor$no, pvalue %in% min(pvalue), p)` to
`r subset(ri_cor$no, pvalue %in% max(pvalue), p)`.
These medium to large effect sizes imply that there are stable, trait-like
differences between persons on these factors.
This suggests that individuals who have more symptoms on one of these factors,
in general, are also more likely to be symptomatic on the other factors.
Additionally, the burdensomeness, belongingness, hopelessness, and depression
random intercepts all had significant variance with suicidal ideation,
(*r*s =
`r subset(ri_cor$yes, std.all %in% min(std.all), r)` to
`r subset(ri_cor$yes, std.all %in% max(std.all), r)`,
*p*s =
`r subset(ri_cor$yes, pvalue %in% min(pvalue), p)` to
`r subset(ri_cor$yes, pvalue %in% max(pvalue), p)`),
with medium effects.
This implies that in general, people who report lower levels of belongingness or
higher levels of burdensomeness, hopelessness, or depression, are also more
likely to report higher levels of suicidal ideation.
The final RI-CLPM model is shown in Figure \@ref(fig:riclpm-fig).
The within-person, or state-like correlations, are also presented in Table
\@ref(tab:riclpm-cor).
Regarding the within-level variance, at T1, burdensomeness was positively
correlated with belongingness, depression, and suicidal ideation.
Suicidal ideation was also positively correlated with belongingness,
hopelessness, and depression.
At T2--T5, all variables were positively correlated with each other, ranging
from medium to large effect sizes.


### Autoregressive Effects

Regarding the state-like within-person part of the model, standardised estimates
of the autoregressive and cross-lagged paths are shown in Table
\@ref(tab:riclpm-arcl).
After the between person stability was partialed out, the autoregressive paths
for burdensomeness were significant at times
`r subset(within_fit$ar, rhs %in% "pb", spread)` ($\beta$s =
`r subset(within_fit$ar, rhs %in% "pb", B_min)` to
`r subset(within_fit$ar, rhs %in% "pb", B_max)`,
*p*s
`r subset(within_fit$ar, rhs %in% "pb", p_min)` to
`r subset(within_fit$ar, rhs %in% "pb", p_max)`).
The autoregressive paths for belongingness were significant at times
`r subset(within_fit$ar, rhs %in% "tb", spread)` ($\beta$s =
`r subset(within_fit$ar, rhs %in% "tb", B_min)` to
`r subset(within_fit$ar, rhs %in% "tb", B_max)`,
*p*s
`r subset(within_fit$ar, rhs %in% "tb", p_min)` to
`r subset(within_fit$ar, rhs %in% "tb", p_max)`).
The autoregressive paths for hopelessness were significant at times
`r subset(within_fit$ar, rhs %in% "bhs", spread)` ($\beta$s =
`r subset(within_fit$ar, rhs %in% "bhs", B_min)` to
`r subset(within_fit$ar, rhs %in% "bhs", B_max)`,
*p*s
`r subset(within_fit$ar, rhs %in% "bhs", p_min)` to
`r subset(within_fit$ar, rhs %in% "bhs", p_max)`).
The autoregressive paths for depression were significant at times
`r subset(within_fit$ar, rhs %in% "dep", spread)` ($\beta$s =
`r subset(within_fit$ar, rhs %in% "dep", B_min)` to
`r subset(within_fit$ar, rhs %in% "dep", B_max)`,
*p*s
`r subset(within_fit$ar, rhs %in% "dep", p_min)` to
`r subset(within_fit$ar, rhs %in% "dep", p_max)`).
The autoregressive paths for suicidal ideation were significant at times
`r subset(within_fit$ar, rhs %in% "si", spread)` ($\beta$s =
`r subset(within_fit$ar, rhs %in% "si", B_min)` to
`r subset(within_fit$ar, rhs %in% "si", B_max)`,
*p*s
`r subset(within_fit$ar, rhs %in% "si", p_min)` to
`r subset(within_fit$ar, rhs %in% "si", p_max)`).


### Cross-Lagged Effects
Regarding the cross-lagged paths, burdensomeness to belongingness was
significant at
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "tb", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "tb", B_max)`,
*p* =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "tb", p_max)`).
However, the reverse paths were non-significant.
For burdensomeness to hopelessness, significant paths were found at
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "bhs", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "bhs", B_min)` to
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "bhs", B_max)`,
*p*s
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "bhs", p_min)` to
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "bhs", p_max)`).
Whilst the reverse paths from hopelessness to burdensomeness were significant at
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "pb", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "pb", B_min)` to
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "pb", B_max)`,
*p*s
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "pb", p_min)` to
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "pb", p_max)`),
and showed marginally stronger effects.
The paths from burdensomeness to depression was significant at
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "dep", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "dep", B_min)` to
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "dep", B_max)`,
*p*s
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "dep", p_min)` to
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "dep", p_max)`).
The only significant reverse path between depression and burdensomeness was at
`r subset(within_fit$cl, rhs %in% "dep" & lhs %in% "pb", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "dep" & lhs %in% "pb", B_max)`,
*p*s =
`r subset(within_fit$cl, rhs %in% "dep" & lhs %in% "pb", p_min)`).
There was also one significant path from burdensomeness to suicidal ideation at
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "si", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "si", B_max)`,
*p*s =
`r subset(within_fit$cl, rhs %in% "pb" & lhs %in% "si", p_max)`).
However, two reverse paths from suicidal ideation to burdensomeness were
significant at
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "pb", spread)`,
($\beta$s =
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "pb", B_min)` to
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "pb", B_max)`
*p*s
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "pb", p_min)` to
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "pb", p_max)`),
although with comparatively smaller effects.


Regarding the cross-lagged paths for hopelessness, one path to belongingness was
significant at
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "tb", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "tb", B_min)`,
*p* =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "tb", p_max)`).
However, no belongingness to hopelessness paths were significant.
For hopelessness to depression, significant paths were found at
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "dep", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "dep", B_min)` to
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "dep", B_max)`,
*p*s
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "dep", p_min)` to
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "dep", p_max)`).
No depression to hopelessness paths were significant.
One path from hopelessness to suicidal ideation was significant at
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "si", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "si", B_max)`,
*p* =
`r subset(within_fit$cl, rhs %in% "bhs" & lhs %in% "si", p_max)`).
The path from suicidal ideation to hopelessness was significant at
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "bhs", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "bhs", B_min)`
*p* =
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "bhs", p_min)`),
although showed a smaller effect.
The cross-lagged paths for suicidal ideation to depression was significant at
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "dep", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "dep", B_min)`,
*p*s =
`r subset(within_fit$cl, rhs %in% "si" & lhs %in% "dep", p_min)`).
However, the reverse depression to suicidal ideation paths were non-significant.
And finally, one cross-lagged paths was significant for belongingness to
suicidal ideation at
`r subset(within_fit$cl, rhs %in% "tb" & lhs %in% "si", spread)`
($\beta$s =
`r subset(within_fit$cl, rhs %in% "tb" & lhs %in% "si", B_min)`,
*p*s =
`r subset(within_fit$cl, rhs %in% "tb" & lhs %in% "si", p_min)`).
There were no significant reverse paths.
Although the belongingness to suicidal ideation path effect size was small, this
was the only non-reciprocal path to suicidal ideation found in the data.


# Discussion

## Main findings

The present study used a naturalistic, longitudinal design to explore the
relationships between the variables proposed by the ITS to be causally
predictive in the development and treatment of desire for suicide: thwarted
belongingness, perceived burdensomeness, and hopelessness [@vanorden2010].
Furthermore, the potential confounding effects of depression on suicidal
ideation were controlled at each timepoint.
To achieve this, we used a RI-CLPM, a methodology that partitions the
between-person (trait-like) and within-person (state-like) dynamic processes.
Regarding the between-person effects, all ITS variables and depression had
significant variance with each other and suicidal ideation.
We found that participants who reported higher severity on one factor (e.g.,
burdensomeness) also tended to report higher severity on another factor (e.g.,
suicidal ideation).
Regarding the within-person dynamics processes, our results showed that the ITS
propositions of perceived burdensomeness, thwarted belongingness, and
hopelessness as temporally predictive of suicidal ideation was partially
supported.
However, in contrast to the propositions of the ITS, the current findings
provide evidence of a bidirectional relationship between suicidal ideation to
burdensomeness and hopelessness [@vanorden2010; @joiner2005].
Whilst the reciprocal relationships differ from those proposed by the ITS, a
small body of longitudinal research has found relationships between suicidal
ideation to burdensomeness similar to our results [@abbott2021; @rogers2019;
@wu2020].
However, few other studies have found a relationship where thwarted
belongingness was positively associated with suicidal ideation [@kyron2018,
@czyz2019a].
Although unlike our findings that showed only thwarted belongingness predicted
suicidal ideation during one lagged time period, @kyron2018 found there was a
reciprocal relationship between these two factors at each measurement occasion.
Whereas @czyz2019a found that the interaction between thwarted belongingness and
burdensomeness or hopelessness predicted next day suicidal ideation.
One other study has also found relationships where hopelessness has predicted
suicidal ideation at subsequent timepoints [@kleiman2017].
Some of the differences between our findings and the aforementioned research may
be due to different analytic designs as well as differing variables, number of
waves, and lag between timepoints.
However, results are largely consistent.
That is, whilst interpersonal factors do have an influence on suicidal ideation,
the reverse has also been found, and the autoregressive influences on suicidal
ideation may be more consistent than those predicted by other factors.


Stepping through the effects in our study, from session one to two, the
cross-lagged effect of suicidal ideation predicted hopelessness, burdensomeness,
and depression.
However, the effect of hopelessness on burdensomeness was stronger than both the
respective cross-lagged and autoregressive effects of suicidal ideation and
burdensomeness at this timepoint.
Both suicidal ideation and hopelessness also had significant autoregressive
effects of similar magnitude.
Whereas no significant autoregressive effects were found for belongingness or
depression between session one and two.
From session two to three, suicidal ideation and hopelessness both had
significant autoregressive effects and significantly predicted severity of
burdensomeness, with hopelessness again showing the stronger effect size.
Whilst burdensomeness did not have a significant autoregressive effect at this
session, it did predict change in belongingness.
Whereas belongingness had a significant autoregressive effect and a unique
cross-lagged effect on suicidal ideation, albeit with a slightly smaller effect size
than the suicidal ideation autoregressive effect.
Depression only predicted changes in itself.
From session three to four, burdensomeness and hopelessness both had moderate
sized cross-lagged effects on suicidal ideation, as well as each other.
Burdensomeness also had a significant cross-lagged effect on depression.
With the exception of suicidal ideation, all variables had significant autoregressive effects.
From session four to five, burdensomeness had moderate cross-lagged effects on
hopelessness and depression.
Whereas depression had a cross-lagged effect on burdensomeness, and hopelessness
on belongingness.
All variables also had significant autoregressive effects.
Overall, our results indicate that prior severity of suicidal ideation is
important in predicting future severity in a range of other psychological
factors related to suicide, and perhaps most importantly, suicidal ideation
itself.
Whilst the effect of suicidal ideation on the other variables is not consistent
with the ITS, it is consistent with recent findings [@abbott2021; @kyron2018;
@rogers2019; @kleiman2017; @czyz2019a; @wu2020].
One study with adolescent suicide attempters endorsed psychache, hopelessness,
and escape as the three most prominent reasons for suicide [@may2016a].
Although we did not directly measure perceptions of psychological pain or
entrapment, these unmeasured factors could have influenced the effects of
suicidal ideation and contributed to the pattern of our results.
We also found a number of relationships that were predicted by the ITS
[@joiner2005; @vanorden2010].
The effects of belongingness on suicidal ideation and burdensomeness on
belongingness are partially concordant with the ITS.
However, the most consistent effect was seen in the cross-lagged effects
involving hopelessness, which at every timepoint had a significant cross-lagged
effect on burdensomeness or belongingness.
Together the results may have implications for treatment and suggest it may be
important to address hopelessness and suicidal thinking directly, rather than
just through the theoretical change mechanisms of burdensomeness and
belongingness [@joiner2009].


## Implications

### Theoretical

This study adds to the small but growing literature on how well the ITS explains
suicidal ideation longitudinally [@kleiman2017; @rogers2019; @kyron2018;
@abbott2021; @czyz2019a; @zhang2021; @wu2020].
Like these studies, our findings indicate that whilst the ITS variables are
implicated in suicidal ideation, the relationship is more dynamic and less
linear than proposed by the theory [@rogers2019; @joiner2005; @vanorden2010].
Moreover, the significant between- and within-person effects indicate that
individual differences should be considered in assessment and treatment.
To this end, suggestions have been made that the ITS may benefit from
incorporating dynamic processes similar to those proposed by the Fluid
Vulnerability Theory (FVT) [@rogers2019; @bryan2016].
Further, the moderate size of the cross-lagged effects of burdensomeness and
hopelessness were similar to the autoregressive effects of suicidal ideation,
indicating that other contributing mechanisms to suicidal ideation still
remain unresolved.
Incorporating other theoretical models may contribute to improved predictive
accuracy via additional variables not assessed in the current study,
specifically psychache and entrapment [@may2016a].
Research investigating differences between the three most prominent modern
theories of suicide---the ITS [@joiner2005; @vanorden2010], the Three Step
Theory [3ST, @klonsky2015], and the Integrated Motivational-Volitional model
[IMV, @oconnor2018a]---suggests that whilst they may each uniquely contribute to
explaining suicidal ideation, there is also crossover between them [@hagan2019;
@debeurs2019; @ordonez-carrasco2021].
Although results vary between the studies, concurrent associations between
suicidal ideation and hopelessness, psychache, entrapment, burdensomeness, and
belongingness have consistently been found [@kleiman2014a; @hagan2019;
@debeurs2019; @panagioti2012; @tarsafi2015; @troister2010].
Given this, a more integrative and dynamic conceptualisation of suicidal
processes may help advance our understanding of the factors that precipitate and
maintain suicidal ideation, but also factors that counteract or protect against
them.


### Clinical

Regarding the usefulness of the ITS in therapy, the between-person effects and
within-level (cross-sectional) variability generally supports the propositions
of the theory.
That is, higher severity on ITS variables was associated with elevated scores on
other ITS variables and suicidal ideation.
However, the within-person dynamic processes (across waves) were not consistent
in terms of the temporal predictions of the theory [@joiner2009; @vanorden2010].
Whilst our findings do offer some support to the propositions of the ITS in
terms of reductions in belongingness and burdensomeness potentially having a
causal influence on reductions in suicidal ideation during treatment
[@joiner2009], they also indicate that increasing hope and directly targeting
suicidal thinking could be particularly important to address during the outset
of therapy.
Therefore, the relative importance of belongingness and burdensomeness as
primary targets of treatment may need to be considered alongside the potential
causal and reciprocal influences of other factors on suicidal thinking.
Moreover, given that suicidal thinking was the most consistent
predictor of subsequent severity of suicidal thinking, this still leaves a
significant gap in our understanding of what may contribute to changes in
suicidal ideation.


Overall, whilst the ITS may be useful in initial assessment, a broader
conceptualisation of suicide may be needed to help navigate the dynamic
processes in treatment.
Interventions most likely work via multiple processes, and similarly
individuals' needs may be achieved via multiple strategies (e.g., direct work on
suicidal ideation or hopelessness, challenging beliefs related to
burdensomeness).
Assessment regarding the stability or chronicity of suicidal ideation and other
associated risk factors, in addition to the availability of protective factors,
can inform a person-centred, inherently non-categorical approach to coping with
and recovering from suicidal ideation [@pisani2016; @rogers2019; @bryan2016;
@jobes2016].
Most supported interventions for suicide prevention with young people
incorporate practical strategies to help minimise suicidal behaviours, improve
problem-solving and emotion regulation [@mufson2004; @miller2007; @pineda2013;
@asen2012].
These are done within the context of improving the functioning of the natural
support systems (family, schools) [@tang2009; @mufson2004; @miller2007;
@pineda2013; @asen2012] and may be important potential targets for early in
treatment [@foster2017].
One common element across interventions is the use of some type of safety plan
[@mufson2004; @miller2007; @pineda2013; @asen2012; @bateman2013a; @stanley2009].
Safety plans could also be considered as providing a framework for
individualised assessment, formulation, and intervention planning.
Given the pattern of our findings, specifically targeting hopelessness could be
particularly important.
Whilst involving other people in treatment will help increase clients' safety,
it could also contribute to improved problem-solving and the attainment of
meaningful goals [@asen2012; @rathus2014].
Increasing meaning in life has been found to influence the relationship between
hopelessness, ITS variables, and suicidal ideation [@kleiman2013; @kleiman2013a;
@marco2020; @marco2016; @marco2017].
Two therapeutic approaches that have been used to treat suicidal ideation that
explicitly target values are dialectical behaviour therapy [@rathus2014] and
acceptance and commitment therapy [@ducasse2018].
Therefore, interventions that increase an awareness of the underlying functions
of suicidal ideation, with the explicit and direct aim of developing effective
interpersonal and intrapersonal coping strategies, and identifying and
developing meaningful and values-based goals and behaviours may be the most
helpful in reducing suicidal ideation.


## Limitations and future directions

There were a number of limitations to our study.
First, the study used a convenience sample accessing a suicide prevention
program providing services to young people deemed to be at mild-to-moderate
severity.
Therefore our findings may not be generalisable to more severe presentations or
older age groups.
Second, the treatment approach was based on a cognitive behavioural therapy
framework tailored for suicide prevention [CBT-SP, @stanley2009].
Although a detailed summary of this approach is beyond the scope of this
article, some key features of CBT-SP include the implementation of a safety
plan, building hope, and using a case formulation-based approach to
collaboratively choose suitable targets of intervention [@stanley2009].
Further, given therapists were able to draw on other approaches in their work,
it is not known how closely they adhered to the CBT-SP framework.
Overall, this may have led to heterogeneous goals and interventions, with the
focus on ITS factors varying during and between sessions, potentially
influencing our results.
As such, treatments based alternative theoretical orientations, or interventions
that focused more specifically on belonging and burden, may have yielded
different results.
Third, the ITS specifies that suicidal ideation is the result of the three-way
interaction between thwarted belongingness, burdensomeness, and hopelessness.
However, due to the limitations of sample size, we were not able to test this
interaction.
Third, the ITS specifies that suicidal ideation is the result of the three-way
interaction between thwarted belongingness, burdensomeness, and hopelessness.
However, due to the limitations of the software we used [@ozkok2021], we were
not able to test this interaction.
Fourth, there may have been issues related to psychometric measurement that
contributed to these findings.
For example, one recent study has suggested that the INQ-15 [@vanorden2012] may
have a third factor, perceived isolation, made up from the thwarted
belongingness items [@hunt2020], or other unmeasured factors such as psychache
and escape, that could be more predictive of suicidal ideation [@may2016a].
Similarly, more waves and shorter lags may have given a more granular view of
the dynamic processes contributing to the maintenance and treatment of suicidal
ideation.
Future studies should seek to address the limitations outlined above, and
longitudinally analyse additional relationships proposed by the ITS and other
theories of suicide across larger and more diverse samples.


## Conclusion

To the best of our knowledge, this study is one of the most comprehensive
longitudinal analysis of the ITS in a clinical sample of young people
experiencing suicidal ideation.
Our findings partially support the propositions of the ITS, whereby thwarted
belongingness, perceived burdensomeness, and hopelessness are predictive of
suicidal ideation [@vanorden2010].
However, in contrast to the theory, prior suicidal ideation more consistently
predicted subsequent suicidal ideation, as well as hopelessness and perceived
burdensomeness [@vanorden2010].
Whilst the ITS could be important in understanding the process of suicidal
ideation and therapy, developments in the field may prosper from a more dynamic
and theoretically integrative approach to conceptualising the risk and
protective factors of suicide.



\newpage

# Data Transparency

The data reported in this manuscript have been previously published and were
collected as part of a larger data collection (at one or more points in time).
Findings from the data collection have been reported in separate manuscripts.
MS 1 (published) tested whether changes in perceived burdensomeness (PB) and
thwarted belongingness (TB) mediated the effects of changes in depression and
hopelessness on suicide risk.
This is currently the only published work and was based on a much smaller sample
size (*N* = 226), fewer variables, and different analyses.
MS 2 (under review) identified three latent classes of suicidal young people
that were distinguished by severity of burdensomeness, belongingness,
hopelessness, suicidality, depression, anxiety, stress, and severity and
frequency of nonsuicidal self-injury.
MS 3 (the current manuscript) focuses on the relationships between
burdensomeness, belongingness, hopelessness, depression, and suicidality over
time (time~n~ to time~n+1~).



\newpage

# References {.tabset}

\setlength{\parindent}{-0.2in} \setlength{\leftskip}{0.2in}
\setlength{\parskip}{8pt} \vspace*{-0.2in} \noindent

<div custom-style=Bibliography> <div id="refs"></div> </div>

\newpage

# Table: Desc

(ref:descr) Descriptive statistics of session frequency, baseline characteristics, and scores on relevant auxiliary variables.

(ref:descr-ft) ^a^Due to low sample proportion of non-binary participants (`r subset(p$n, sex %in% "other", prc)`%), participants' identifying as non-binary had their values on the gender variable treated as missing. ISAS = Inventory of Statements about Self-injury; *N* = Total participants with available data; % Missing = percent of missing data based on total sample size (*Total* = `r paste0(n_distinct(phd_fin_wide$ID))` participants).


```{r, descr, include = TRUE, results = "show", warning = FALSE, tidy = FALSE}
riclpm_des_t1 %>%
  filter(!name %in% "rel_stat") %>%
  select(namep, m_sd, range, N, miss) %>%
  kbl(
    col.names = c(
      "", "*n(%)*", "Range", "*N*", "% Missing"
    ),
    align = "lcccc",
    caption = "(ref:descr)"
  ) %>%
  kable_styling(
    font_size = 8
  ) %>%
  footnote(
    general = "(ref:descr-ft)",
    general_title = "Note.",
    footnote_as_chunk = TRUE
  )
```


\newpage

# Table: Means of study variables

(ref:means) Means, standard deviations, and ranges of variables used in the RI-CLPM.

(ref:means-ft) T~*n*~ = Time~*n*~; *N* = sample size observed data at T~*n*~; % Missing = percentage of missing data in comparison to the sample size at Time 1 (*N* = `r paste0(n_distinct(phd_fin_wide$ID))`).


```{r, means, include = TRUE, results = "show", warning = FALSE}
riclpm_des_t15 %>%
  kbl(
    col.names = c(
      "", rep(c("*M(SD)*", "Range", "*N*", "% Missing"), 5)
    ),
    align = c("l", rep("c", 25)),
    caption = "(ref:means)"
  ) %>%
  add_header_above(
    c("", "T1" = 4, "T2" = 4,
      "T3" = 4, "T4" = 4, "T5" = 4
      )
  ) %>%
  kable_styling(
    font_size = 8
  ) %>%
  footnote(
    general = "(ref:means-ft)",
    general_title = "Note.",
    footnote_as_chunk = TRUE
  )
```

\newpage

# Table: Correlations


(ref:riclpm-cor) Summary of Correlations Between and Within Person Variables


(ref:riclpm-cor-ft) All variables freely estimated. RI = Random intercept, representing between-person or trait-like variability. T~*n*~ = Time~*n*~, representing the within-person or state-like variability after taking into account the between person effects. PB = Perceived TB = Thwarted Belongingness; BHS = Hopelessness; DEP = Depression; SI = Suicidal Ideation. ^\*\*\*^*p* < .001; ^\*\*^*p* < .01; ^\*^*p* < .05.


```{r, riclpm-cor, include = TRUE, results = "show", warning = FALSE}
riclpm_cor %>%
  kbl(
    col.names = c(
      "", "RI", paste0("T", 1:5)
    ),
    align = "lcccccc",
    caption = "(ref:riclpm-cor)"
  ) %>%
  kable_styling(
    font_size = 8
  ) %>%
  footnote(
    general = "(ref:riclpm-cor-ft)",
    general_title = "Note.",
    footnote_as_chunk = TRUE
  )
```


\newpage

# Table: Autoregressive and Cross-Lagged Paths


(ref:riclpm-arcl) Standardised Autoregressive and Cross-Lagged Paths.

(ref:riclpm-arcl-ft) PB = Perceived TB = Thwarted Belongingness; BHS = Hopelessness; DEP = Depression; SI = Suicidal Ideation. Due to the large number of coefficients in the table and to aid interpretation, bold is used to highlight statistically significant effects. ^\*\*\*^*p* < .001; ^\*\*^*p* < .01; ^\*^*p* < .05.


```{r, riclpm-arcl, include = TRUE, results = "show", warning = FALSE}
riclpm_arcl %>%
  select(-c(path, order)) %>%
  kbl(
    col.names = c(
      "Model path", "",
      rep(c("&beta;", "*SE*", "95% CI"), 4)
    ),
    align = c("l", "l", rep("c", 12)),
    caption = "(ref:riclpm-arcl)"
  ) %>%
  add_header_above(
    header = c(
      "", "",
      "T1 → T2" = 3,
      "T2 → T3" = 3,
      "T3 → T4" = 3,
      "T4 → T5" = 3
    )
  ) %>%
  collapse_rows(columns = 1, valign = "top") %>%
  kable_styling(
    font_size = 8
  ) %>%
  footnote(
    general = "(ref:riclpm-arcl-ft)",
    general_title = "Note.",
    footnote_as_chunk = TRUE
  )
```


\newpage


# Figure 1: Statistical Model

(ref:riclpm-mod) Illustration of a Random-Intercept Cross-Lagged Path Model (RI-CLPM). Prefix B denotes between-person effects. Prefix W denotes within-person effects. Squares represent observed variables and circles represent latent variables straight arrows represent direct effects and curved lines represent correlations between variables. Only two predictor variables are shown for simplicity. PB = Perceived Burdensomeness. SI = Suicidal Ideation. T~*n*~ = Time~*n*~. Auxiliary Variables = Auxiliary variables used in the saturated correlates model of managing missing data for full information maximum likelihood estimation. For simplicity, all auxiliary variables are assumed to be contained with the box on the diagram. The saturated correlates model requires that the auxiliary variables (e.g., Acquired Capability, age) correlate with (1) one another, (2) manifest predictor variables, and (3) the residual terms of the manifest variables. The auxiliary variables never correlate with a latent variable or with a latent variable residual term [@enders2010].


```{r, riclpm-mod, fig.cap = "(ref:riclpm-mod)", include = TRUE, results = "show", warning = FALSE}
include_graphics(
  ifelse(
    knitr::pandoc_to("docx"),
    "./figures/graphviz/model_steveroush_edit.pdf",
    "./figures/graphviz/model_steveroush_edit.png"
  )
)

```


\newpage

# Figure 2: Results Model

(ref:riclpm-fig) Prefix 'B' denotes between-person effects. Prefix 'W' denotes within-person effects. tb~*n*~ = Thwarted Belongingness at time *n*; pb~*n*~ = Perceived Burdensomeness at time ~*n*~; si~*n*~ = Suicidal Ideation at time *n*; bhs~*n*~ = Hopelessness at time *n*; dep~*n*~ = Depression at time *n*. Only statistically significant paths are graphed for simplicity. For the between-person part of the model (left of figure), correlation coefficients are shown. For the within-person autoregressive (solid lines) and cross-lagged (dashed lines) portion of the model (right of figure), standardised coefficients are shown and can be found nearest to the terminating edge of the path (near its arrow). See Table \@ref(tab:riclpm-arcl) for coefficient confidence intervals and *p* values, and Table \@ref(tab:riclpm-cor) for variances and covariances.


```{r, riclpm-fig, fig.cap = "(ref:riclpm-fig)", include = TRUE, results = "show", warning = FALSE}
include_graphics(
  ifelse(knitr::pandoc_to("docx"),
    "./figures/graphviz/combi3.pdf",
    "./figures/graphviz/combi3.png"
  )
)

```


[^1]: Whether this assumption is tenable can be tested empirically [cf.
      @mulder2021]. In the current study, this assumption was tested, however
      the model failed to converge.

[^2]: When the model was specified via the 'semTools' package, the software
      provided the warning that the "residuals of the observed variables is not
      positive definite". This warning may be related to correlating auxiliary
      variables with residuals of variables that have zero residual variance
      because they are treated as single-indicator factors to enter the model
      [@jorgensen2021a]. To investigate this warning further we incorporated the
      auxiliary variables directly into the model syntax via the 'lavaan'
      package (bypassing the 'semTools' package). No warnings were generated by
      the software and the model was accepted as is. Additionally, a sensitivity
      analysis was run with and without the auxiliary variables. Whilst
      estimates did not substantially change, the software provided the warning
      "that the covariance matrix of the latent variables is not positive
      definite", indicating that auxiliary variables are required to make valid
      statistical inferences [@blozis2013]. Results with auxiliary variables
      using the 'semTools' package are reported.

[^3]: All code used for this manuscript is available at the github repository
      https://github.com/atanasj/riclpm_public. Whilst data is not publicly
      available, this repository also provides information about how the
      interested reader can apply to the data custodians for access to the data.

[^4]: See 'Missing Data' subsection below for further information about
      how missingness on this measure was handled.

\newpage


# Supplementary Material: Correlations between study and auxiliary variables

(ref:corrs) Descriptive statistics for session frequency, baseline characteristics, and scores on relevant auxiliary variables.


(ref:corrs-ft) Subscript t*n* = Time~*n*~. pb = Perceived Burdensomeness, tb = Thwarted Belongingness; bhs = Hopelessness; dep = Depression; si = Suicidal Ideation. AC = Acquired Capability measured at time 1. *N*ses = Number of sessions attended. SH-Inter = Interpersonal reasons for self-injury; SH-Intra = Intrapersonal reasons for self-injury. Hx prefix denotes a personal history. SH = Deliberate self-injury; Tr = Trauma, SA = one or more suicide attempts; liv_fam = Living with family. Past-Med = current or past pharmacotherapy; Past-Pysc = previous engagement in psychological interventions. ^\*\*\*^*p* < .001; ^\*\*^*p* < .01; ^\*^*p* < .05.


```{r corrs, include = TRUE, results = "show", warning = FALSE}

.var <-
  c(
    unlist(
      map(
        c("pb", "tb", "bhs", "dep", "si"),
        ~ paste0(., "<sub>", "t", 1:5, "</sub>")
      )
    ),
    "AC",
    "Age", "Sex", "*N*ses", "SH-Inter", "SH-Intra",
    paste0("Hx-", c("SH", "Tr", "SA")),
    "liv-fam",
    paste0("Past", c("Med", "Psyc"))
  )

corr_mat %>%
  mutate(
    var = .var, .before = 1
  ) %>%
 select(-rowname) %>%
  kbl(
    ,
    col.names = c(
      "", .var
    ),
    align = c("l", rep("c", length(.var))),
    caption = "(ref:corrs)"
    ) %>%
  kable_styling(
    font_size = 8
  ) %>%
  footnote(
    general = "(ref:corrs-ft)",
    general_title = "Note.",
    footnote_as_chunk = TRUE
  ) %>%
  column_spec(1, bold = TRUE) %>%
  column_spec(1:38, width = "0.5cm")


```


```{r mar-fig, include = TRUE, results = "asis", warning = FALSE, eval = knitr::pandoc_to("html")}
cat(paste0(
  c(
    "\\newpage",
    "# Figure 3: MAR"
  )),
sep = "\n\n\n")
```

```{r, mar-fig-incl, results = "show", eval = knitr::pandoc_to("html")}
include_graphics("./figures/miss_plots_p.png")
```


```{r repro-header, include = TRUE, results = "asis", warning = FALSE, eval = knitr::pandoc_to("html")}
## NOTE this only gets run on html output
cat(paste0(
  c(
    "\\newpage",
    "# Reproducibility",
    "<details><summary> receipt</summary>"
  )),
sep = "\n\n\n")
```

```{r, reproducibility-receipt, results = "show", eval = knitr::pandoc_to("html")}
## datetime
Sys.time()
## repository
git2r::repository()
## session info
sessionInfo()
```


```{r repro-end, include = TRUE, results = "asis", warning = FALSE, eval = knitr::pandoc_to("html")}
cat(paste0(
  c(
    "",
    "</details>"
  )),
  sep = "\n\n\n"
  )
```

---
abstract: |
  ***Objective:***
  The Interpersonal Theory of Suicide (ITS) predicts perceived burdensomeness,
  thwarted belongingness, and hopelessness lead to suicidal ideation and
  recommends burdensomeness and belongingness should be the targets of
  treatment.
  Limited research has tested if burdensomeness and belongingness temporally
  predict suicidal ideation during treatment.
  This study examined the bidirectional relationships between burdensomeness,
  belongingness, hopelessness, depression, and suicidal ideation in young people
  seeking treatment for suicide related behaviours.
  ***Method:***
  A sample of
  `r paste0(n_distinct(phd_fin_wide$ID))`
  Australian young people
  (`r subset(p$n, sex %in% "female", prc)`%
  females, *M*~age~ =
  `r sprintf("%.2f", mean(phd_fin_wide$age, na.rm = TRUE))`
  [*SD* = `r sprintf("%.2f", sd(phd_fin_wide$age, na.rm = TRUE))`])
  completed measures of burdensomeness, belongingness, hopelessness, depression,
  and suicidal ideation at each session of treatment
  (*M~sessions~* = `r sprintf("%.2f", mean(phd_fin_wide$cov_sess, na.rm = TRUE))`
  [*SD* = `r sprintf("%.2f", sd(phd_fin_wide$cov_sess, na.rm = TRUE))`]).
  A random-intercept cross-lagged panel model (RI-CLPM) examined the within-person
  direction of effects across the first five occasions of treatment.
  ***Results:***
  Autoregressive paths showed hopelessness had carryover effects across all
  timepoints.
  All other variables had carryover effects at four timepoints.
  Cross-lagged paths varied, with suicidal ideation predicting depression,
  burdensomeness and hopelessness.
  Belongingness, burdensomeness and hopelessness predicted suicidal ideation on
  one occasion.
  Hopelessness predicted burdensomeness and depression at three timepoints, and
  predicted belongingness on one occasion.
  ***Conclusions:***
  Results are partially consistent with the ITS, but in contrast to the theory
  the most consistent predictor on suicidal ideation was prior suicidal
  ideation.
  Prior levels of hopelessness, belongingness and burdensomeness did influence
  suicidal ideation at some timepoints, but the most consistent effects were
  from hopelessness towards burdensomeness.
  Theoretical and treatment implications for these findings are discussed,
  particularly the need to directly address hopelessness in treatment.

---