The Child-to-Parent Violence Functions Scale (CPV-F): Development and Validation

The function (i.e., the motivation) of child-to-parent violence (CPV) is an important consideration for intervention but under researched, primarily due to a lack of appropriate measurement tools. The current study aimed to develop and validate a caregiver-report measure of the function of CPV (the Child-to-Parent Violence Functions Scale [CPV-F]). One-hundred-and-twenty-one caregivers (94% female) ranging from 27 to 68 years of age (M = 45.36, SD = 8.35) completed an online survey reporting on experiences of CPV from a young person, who were mostly male (63%) and aged between 5 and 24 years (M = 12.71, SD = 4.77). The current study shows that the motivation for CPV varies across three related but distinct functions: Reactive (i.e., in response to perceived or actual threat, transgression, or intrusion), Affective (i.e., driven by internal frustration, fear, or emotional conflict), and Proactive (i.e., instrumental, callous, and planned). The CPV-F demonstrated predictive and concurrent validity, as well as adequate reliability across subscales. Future research should consider the function of CPV, as it may impact the relevance of risk factors. Moving forward, the CPV-F could be used for comprehensive investigative profiling, with a focus on parent and dyadic factors, to resolve heterogeneity in the field. Such factors are crucial to intervention yet under explored. As a caregiver-report measure, the CPV-F is well-positioned to aid in these investigations.


Introduction
Child-to-parent violence (CPV) is the repeated use of physical or psychological (including verbal and emotional) violence by a child towards a caregiver and is a pervasive community issue (Pereira et al., 2017). Prevalence rates of CPV vary drastically between studies (McCloud, 2017). Depending on how CPV is operationalised, between 5 and 21 percent of young people may use CPV . Within Australia, conservative estimates of incidence suggest that approximately 16% of parents may experience CPV in any year (Simmons et al., 2019). Some definitions mandate that CPV is primarily driven by motives of dominance and control. To illustrate, Cottrell (2001, p.3) defines CPV as "any act of a child that is intended to cause physical, psychological, or financial damage to gain power and control over a parent". Yet, it is evident that young people may use CPV for a range of reasons, many of which are not congruent with dominance, such as retaliation and anxiety (Nock & Kazdin, 2002). CPV may differ in form (the what), as well as function (the why). Indeed, a recent review identified that CPV may have both proactive and reactive functions (Harries et al., n.d.). Proactive aggression is often instrumental, for tangible or social gain (such as dominance over a parent), whereas reactive aggression is seen to be driven by negative affect (e.g. anger, fear) in response to provocation or perceived threat (Dodge, 1991), or internal frustration (Blair, 2013;Smeets et al., 2017). However, reactive aggression is sometimes factorised as two distinct dimensions: reactive aggression due to provocation, and reactive aggression due to internal frustration (e.g., Smeets 1 3 et al., 2017). Importantly, the function of aggression may be a way to identify sub-types of those who use CPV and improve intervention responsivity.
To date, the method by which proactive and reactive aggression have been measured in CPV research limits the applicability of findings to clinical practice. Of the few studies available, most have utilised the Reactive-Proactive Aggression Questionnaire (RPQ; e.g., Calvete et al., 2013b;McCloud, 2017), which measures the function of general aggression, but not CPV specifically. There is evidence that the function of aggression may be influenced by the nature of the dyad within which it occurs (Dodge et al., 1990b;Hubbard et al., 2001;Matthys et al., 1995;Tucker et al., 2013). Specifically, Hubbard et al. (2001) demonstrated that engagement in proactive aggression was partially driven by characteristics of the victim (i.e., their likelihood to be submissive). Thus, it is important that measures of aggression are specific to the subject of the aggression.

Function of CPV and Intervention
In general delinquency, the motivations for behaviour can identify sub-types of offenders (e.g. firesetting; Kolko & Kazdin, 1991). Recently, Contreras et al. (2020b) demonstrated that the reactive or proactive nature of CPV may differentiate young people who use CPV on a number of social-cognitive factors. Contreras et al. found that proactive CPV was positively and uniquely associated with attitudes which justified violence, as well as greater anticipation of positive outcomes from aggressive acts. On the other hand, reactive CPV was positively related to anger and the accessibility of aggressive responses. Together, this suggests that the motivations for aggression may characterise unique profiles of young people who use CPV with different intervention needs.
Effective interventions are those which can be responsive to individual participant needs (Andrews et al., 2011). Knowledge pertaining to the function of CPV is valuable to improving the responsivity of intervention, where current programs are limited in effectiveness (e.g., Step Up; Gilman & Walker, 2019). Proactive and reactive aggression are facilitated by distinct cognitive processes and biases (See Hubbard et al., 2010 for a review), each requiring tailored intervention (McAdams, 2002). For example, reactive aggression may respond best to interventions focusing on impulse control, whereas proactive aggression may be reduced through a focus on consequences and social skills training (McAdams, 2002). The assessment of proactive and reactive CPV could also aid in ensuring the delivery of risk-appropriate intensity of intervention and allocation of intervention resources (Andrews et al., 2011). The presence of proactive aggression can increase the risk of behavioural disorder development/ diagnosis and is a marker for more severe cases (Smeets et al., 2017). Indeed, proactive aggression is characteristic of young people with callous-unemotional personality traits, likely due to its cold and calculated nature (Kerig & Stellwagen, 2010;Lozier et al., 2014). In sum, the function of their aggression can provide intervention-relevant information regarding the characteristics and clinical needs of the young person.

Current Measures of CPV Function
Further empirical investigation into the function of CPV has clinical utility but is limited by a dearth of appropriate measurement tools. Currently, only two quantitative measures of proactive and reactive CPV exist. The Reasons subscale of the Child-to-Parent Violence Questionnaire (CPV-Q; Contreras et al., 2019) distinguishes between instrumental and reactive reasons for CPV with adequate reliability (Contreras et al. 2019(Contreras et al. , 2020b. However, until recently, the CPV-Q was only available as young person self-report. This restricted its use to samples of young people of a validated age (as opposed to parents who could report on a broader age range, without adaption to the language of items), or complex research designs using dyadic sampling methods (i.e., sampling caregivers as well as the young person), which are resource-heavy and often yield small sample sizes. Further, self-reports of aggression are susceptible to under-perception, and thus under-reporting (Fernández-González et al., 2013;Lochman & Dodge, 1998). The Child-to-Parent Aggression Questionnaire (CPAQ; Calvete et al., 2013a) was also updated and validated to include a reasons subscale which consisted of instrumental, defensive, and affective reasons (Calvete & Orue, 2016;Calvete & Veytia, 2018). However, similar to the CPV-Q, these data were only obtained through youth-report.

The Development of Parent-Report Measures
In understanding the function of CPV, parent-report has several advantages. CPV is evident across a variety of developmental stages, from early childhood to late adolescence (e.g., Nock & Kazdin, 2002 describe a case of CPV involving a 6-year-old). Self-report measures require adaption to suit the developmental stage and ability of the child, whereas a parent-report measure could capture data for a wide variety of ages, without adaption. This also allows for relationships between young person characteristics and parent-related variables to be investigated without sampling dyads. Proactive and reactive aggression have distinct associations with parenting (e.g., harsh parenting; Dodge et al., 1997;Vitaro et al., 2006) and parent-related variables (e.g. substance use; Raine et al., 2006), many of which require further investigation in the CPV literature base as they are understudied or have produced mixed findings (Harries et al., n.d.). Exploring these variables in the context of the function of aggression, and dyadic factors, will aid in understanding potential variability in pathways to CPV (Harries et al., n.d.;Holt & Shon, 2016). Contreras et al. (2020a) recently adapted and validated the CPV-Q for parent-report (CPV-Q-P). Within a sample of Spanish mothers and fathers, the CPV-Q-P possessed adequate psychometric properties, including the 'reasons' subscales (instrumental vs. reactive). However, the reasons subscale is brief and may not capture the proactive-reactive dichotomy in its entirety; only assessing the reason for an aggressive act may instead measure the most frequent topics/ instigators of conflict, rather than the proactive or reactive nature of any aggression involved in that conflict. For example, aggression used in an argument around money could be proactive if the young person believes that this will lead to the parent giving them money, or reactive if the young person believes the parent is being unfair or unjust and they are motivated to be aggressive to relieve their subsequent frustration. Indeed, the function of aggression is multifaceted and not fully determinable from a precipitating event alone, whereby reactive aggressions can have a seemingly proactive reason (Dodge, 1991). Instead, determination of the function of aggression may also include measurement of the physiological state of the young person (the presence of anger/arousal in reactive aggression, or lack of in proactive aggression; Hubbard et al., 2002Hubbard et al., , 2010, the timing of the aggressive act (reactive aggression rapidly follows a trigger, whereas proactive aggression may be delayed; Book et al., 2019;Frijda, 2010;Reidy et al., 2017), the presence of provocation (reactive aggression, unlike proactive aggression, is in response to real or perceived threat; Dodge et al., 1990a;Ostrov & Crick, 2007), and the purpose of the aggression (proactive aggression is goal-oriented, such as the attainment of an object; Dodge et al., 1990a;Ostrov & Crick, 2007).
While the form of aggression is very easily identifiable to an observer, the function can be ambiguous and harder to distinguish (Kempes et al., 2005). The agent of an aggressive act is arguably best placed to inform on the motivation they had for the behaviour (Raine et al., 2006). Nonetheless, observational studies have reliably coded reactive and proactive aggressions using contextual indicators (Boivin et al., 1995;Dodge et al., 1990a;Hart & Ostrov, 2013;Ostrov & Crick, 2007). Further to the validity of observational measures, teacher-report measures are commonly used (Polman et al., 2007) and show good reliability (e.g., Polman et al., 2009). Indeed, reactive and proactive have unique qualities evident to outside observers (Dodge, 1991;Kempes et al., 2005). Thus, parent-report measures for the function of CPV are valuable and feasible, yet there is currently a dearth of appropriate options for this vital consideration within the field. Currently, only one parent-report measure is available (the CPV-Q reasons subscale) and is limited to measuring the reasons for aggression, rather than a full indication of function. As such, the current study aims to develop and validate a novel and more comprehensive, parent-report scale of proactive-reactive CPV. The new measure (Childto-Parent Abuse Functions Scale; CPV-F) will be piloted alongside an existing parent-report measure of reactiveproactive general aggression, as well as known predictors of proactive violence (e.g., callous-unemotional traits).

Participants
An Australian community sample was acquired through the use of targeted social media advertisements on 'parent-child conflict' research. Participants were 121 caregivers of young people, who met the criteria for experiencing CPV on the Abusive Behaviour by Children -Indices (i.e., they scored 16 or greater; Simmons et al., 2019). Those who did not meet this criterion were excluded. The vast majority of participants were a biological parent of the young person (84%), and 7.5% were a step, foster, or adoptive parent. Participants were majority female (94%) and ranged from 27 to 68 years of age (M = 45.36, SD = 8.35). Just over half (52%) were never married, separated, or divorced, and 46% were married. The young people they reported on were mostly male (63%) and were between 5 and 24 years of age (M = 12.71, SD = 4.77). Two (1.7%) young people identified as transgender. The socioeconomic status of the sample was broadly representative of the Australian population, and evenly distributed across the SIEFA Index of Relative Socio-Economic Advantage and Disadvantage percentiles (Median = 41 st percentile, IQR = 46), as well as the Index of Education and Occupation percentiles (Median = 38 th percentile, IQR = 42). Participants were excluded if they were not over the age of 18; if they were not an Australian resident; or if their young person was not aged between 5 and 24 years. The minimum age of five years was selected to exclude any developmentally normal aggression (Lorber et al., 2019), which is primarily due to a lack of language development, before this age. The maximum age of 24 was selected because many young people in Australia continue to live at home after turning 18 (Australian Institute of Family Studies, 2022) and are still considered 'youth' until turning 25. While the age range is board, the function of violence is likely to be less impacted by age than the form.

Demographics
Participants were asked to provide gender and age information for both themselves and the child they identify as using CPV (the target child). Participants were also asked to provide their marital status and relationship with the target child, as well as postcode, any mental health diagnoses for the young person, and if the young person currently lives with them.

The Abusive Behaviour by Children -Indices (ABC-I)
The ABC-I (Simmons et al., 2019) is a measure of childto-parent abuse validated for use with the Australian population. This measure contains nine items measuring three subscales: Physical aggression (e.g., "acted physically aggressively towards you"), verbal aggression (e.g., "shouted or swore at you"), and coercive behaviour (e.g., "stole money or possessions from you"). Participants responded to items using a 6-point rating scale ranging from never to daily. The values on the scale were weighted differentially per item based on severity to distinguish abuse from violence. A score of greater than or equal to 16 indicated abuse within the last 12 months. The ABC-I has been validated on a sample of young people aged 14-25 and shows good criterion and convergent validity, as well as excellent ability to discriminate between abused and non-abused parents (Simmons et al., 2019). The wording of items was adapted to be parent-report as suggested by the authors. In the current study, reliability of the ABC-I was acceptable across verbal (α = 0.82), physical (α = 0.60), and coercive (α = 0.68) subscales (though we note that these are formative, not reflective constructs).

The Child-to-Parent Abuse Functions Scale (CPV-F)
The CPV-F is a measure of reactive and proactive aggression specific to the parent-child relationship and was developed as a part of the current study. Before item reduction, 31 items measured the observable differences between proactive and reactive aggressions (Kempes et al., 2005), centred on four facets apparent during the act of violence: Affect, timing, provocation, and purpose. Participants respond to items on a 5-point Likert scale ranging from 0 (never) to 4 (almost always). Following item reduction, 23 items remained across 3 factors: Reactive, Affective, and Proactive.

The Parent-Report Proactive and Reactive Aggression Questionnaire (PRPA)
The PRPA (Kempes et al., 2006) is a parent-report measure of proactive and reactive general aggression consisting of eleven items (e.g., "the young person is sneaky in order to gain an advantage") rated on a 3-point scale (1 = Never, 3 = Often). The PRPA has been validated on a sample of young people aged 6-12 years, where a two-factor model could be adequately distinguished using parent observations of the young person's behaviour (Kempes et al., 2006). Reliability in the current study was good (Reactive: α = 0.91, Proactive: α = 0.74), similar to use of the scale in past studies (Reactive: α = 0.91, Proactive: α = 0.81; Kempes et al., 2006). The PRPA was used to determine concurrent validity of the CPV-F.

Conflict Tactics Scale (CTS)
Four items were taken from The CTS (Straus et al., 1996) and used to measure psychological (e.g., "shouted or yelled") and physical violence (e.g., "pushed or shoved") against siblings and peers, to assist in the determination of concurrent validity of the CPV-F (i.e., those who reported violence were then administered the PRPA). Items measured the frequency of violence on a 6-point Likert scale ranging from 0 (never) to 5 (daily) and were repeated for both peers and siblings. Reliability of the scale in the current study was excellent for peer (α = 0.92) and sibling (α = 0.91) violence.

The Inventory of Callous-Unemotional Traits (ICU)
The ICU is widely used in screening for callous-Unemotional traits (Frick, 2004). The ICU is a 22-item questionnaire (e.g., "does not care who they hurt to get what they want") which targets four factors underpinning the callousunemotional construct: callous, careless, uncaring, and unemotional (McDonald et al., 2018) and was used in the current study to assess the predictive validity of the CPV-F. Participants respond to each item on a 4-point Likert scale, ranging from 0 (not at all true) to 3 (definitely true). We used a cut-off score of 30 to distinguish high CU traits from low CU traits ( Docherty et al., 2017). The ICU demonstrates good criterion validity in adolescent samples, and good convergent validity in older children (Gao & Zhang, 2016). Other-report versions, such as the parent-report used in the current study, also show comparatively adequate validity and reliability compared to self-report (Cardinale & Marsh, 2017). Reliability in the current study was excellent for the full scale, α = 0.90. Past studies have shown similarly adequate reliability (α = 0.87; Waller et al., 2015).
Prior to validation with caregivers, an early version of the CPV-F was piloted. Participants in the pilot phase were 14 clinical and/or academic experts, who were contacted via email and invited to participate. Participants had authored or co-authored at least one published peer-reviewed paper in the area of violence and aggression (i.e., academic) or had worked in the area of violence intervention (i.e., clinician). Experts had an average of 12 years of experience (SD = 8.28). Most experts worked as both a clinician and an academic (n = 7). Drafted items (n = 31) were then reviewed by participants for face validity, as well as the generation of additional items and the trimming of superfluous items. As this is a measure of a pre-existing construct, it was not necessary to go beyond this (e.g., focus groups). Content validity was assessed using an adapted version of the process described in Zamanzadeh et al. (2015). After providing informed consent, participants ranked items on their relevance and clarity on a 3-point Likert scale (1 = not relevant/clear, 2 = somewhat relevant/clear, 3 = relevant/clear). Participants also provided freeform qualitative feedback on items. Overall, the piloted items demonstrated good content validity, with an average clarity rating (i.e., participants who responded somewhat clear or clear) of 93%, and an average relevance rating of 94.4%. Almost all items underwent minor changes to wording following this process, guided by the qualitative responses provided by participants.

Validation Study
Prior to participant recruitment, ethics approval was attained from Deakin University Human Research Ethics Commitee (DUHREC; ID: 2020-227). Potential participants accessed an online survey hosted on Qualtrics between June and October 2021. As approved by DUHREC, and outlined in the PLS, implied consent was obtained from participants through their choice to continue to the survey after reading the PLS. The survey took approximately 25 min to complete. Participants could leave the survey at any time. Those who completed the survey had the opportunity to enter a draw to win 1 of 10 $50 gift vouchers. Data were analysed using SPSS version 26 (IBM Corp, 2019).

Statistical Power
While there are no power formulas available for factor analysis, between 100-200 observations are sufficient, based on Monte Carlo simulations (MacCallum et al., 1999). The current study has a 4:1 observations to items ratio. While a 10:1 ratio is ideal, a large proportion of studies successfully model with between 2:1 and 5:1, and the average difference in factor loading error between a 5:1 and 10:1 study is only around r = 0.03 (Costello & Osborne, 2005).

Data Cleaning and Preparation
Before item reduction, missing data per item of the CPV-F ranged between 10-15%, with 17% (n = 21) of cases missing at least one value on one item. Little's MCAR test demonstrated that data were missing completely at random (X 2 = 183.05, p = 0.464). In line with best practice for exploratory factor analysis on small samples (McNeish, 2017), all missing values within cases with less than 40% missing data (n = 8) were replaced with the mean score for respective items. Cases missing greater than 40% of items were excluded listwise (n = 13). Missing data for the ICU and PRPA were dealt with using the same strategy, to preserve statistical power. Both scales were missing less than 5% of data. For the ABC-I, there was less than 2% of cases (n = 2) with missing data. Missing values were not replaced, though the cases were retained for analyses and a sum score was still generated.

Exploratory Factor Analysis
An exploratory factor analysis was conducted using the initial 30 items of the CPV-F. Responses to items were primarily non-normally distributed, with positive skewing common for proactive items. As such, we opted to run a Generalised Least Squares model which is less sensitive to departures from normality than other extraction methods (Tellinghuisen, 2008). Analysis of multivariate outliers was conducted by calculating the Malhalanobis distance for each case; 1 multivariate outlier was identified using a cut-off of < 0.001 and removed. Two items did not have a correlation coefficient of greater than 0.30 with any other item in the scale and were removed from the model. The Kaiser-Meyer-Olkin (KMO) value of the final model was classified as meritorious (0.88; Kaiser, 1974), indicating that the data was adequate for factor analysis. Individual KMO values varied but most were above 0.80; one further item was removed as the antiimage correlation was less than 0.50. Bartlett's test of sphericity was statistically significant (p < 0.001), suggesting the data was factorizable.
Extraction and interpretation of these factors was aided by an Oblimin rotation with Kaiser normalisation and was based on previous studies of the construct where it is theoretically and empirically possible to extract either a 2-or 3-factor solution; Reactive aggression can be further factorised into that which is internally-induced (due to frustration) or externally-induced (due to provocation; Blair, 2013;Smeets et al., 2017). One further item was removed during this stage as it loaded evenly across factors and failed to distinguish between them ("The young person overreacts with aggression or violence"; Factor 1: 0.328, Factor 2: 0.413, Factor 3: 0.332). It is likely that this item was too generalised to provide distinction between functions of aggression. In determining the factor structure, a minimum loading of 0.30 was used (as per Peterson, 2000). The 3-factor solution was the best fit for the data (X 2 = 172.93, p = 0.762), compared to a 2-factor solution (X 2 = 205.79, p = 0.531), and was retained. A visual inspection of the scree plot supported the extraction of three factors (see Fig. 1). The 3-factor solution explained 48.36% of the total variance in the model. The first factor was consistent with reactive aggression in response to provocation (labelled 'Reactive'; α = 0.80) and explained 18.54% of the total variance. The second factor reflected a proactive function of aggression (labelled 'Proactive'; α = 0.91) and explained a further 22.07% of total variance. The third and final factor best represented reactive aggression from internal frustration (labelled 'Affective'; α = 0.62) and explained 7.78% of the total variance. Factor loadings of the rotated solution are presented in Table 1.

Descriptive Statistics
The means and standard deviations, as well as any observed gender differences for each of the key variables are presented in Table 2. Boys and girls were reported to use similar levels of physical, verbal, and coercive abuse tactics. Only proactive CPV scores were different, with girls scoring significantly higher than boys.
Correlations between variables used in the regression analyses are presented in Table 3. Consistent with reactive and proactive aggression in other contexts, there was a strong correlation between proactive CPV and reactive CPV (r = 0.68), though a weaker correlation was found between proactive CPV and Affective CPV (r = 0.21) and between reactive and affective CPV functions (r = 0.34).

Regression Analyses
We conducted four regression analyses to explore the predictive and concurrent validity of the CPV-F, controlling for age and gender. The results from each model are presented in Table 4. First, a binomial logistic regression was conducted to explore the association between the function of CPV and CU traits, controlling for the age and gender of the young person. The model was statistically significant (χ 2 (5) = 59.34, p < 0.001) and explained 60% of the variance in CU traits. ROC curve analysis demonstrated that the overall model provides an 'excellent' (borderline 'outstanding'; Hosmer et al., 2013) level of discrimination in determining CU trait categorisation; the area under the ROC curve was 0.898, 95% CI[0.837, 0.958]. Of the five independent variables modelled, two were statistically significant: Age of the young person (B = 0.16, OR = 1.11, p = 0.005) and Proactive CPV (B = 2.69, OR = 14.76, p < 0.001).
Two binomial linear regression models were constructed to explore the association between the function of CPV and reactive and proactive aggression towards others, controlling for the opposing aggression function to account for the strong relationship between reactive and proactive  The young person appears to plan how they will 'get back at me' for things they did not like (e.g., something I said or did) 0.650 19 They are demanding 0.611 9 The young person is devious 0.587 17 After being violent or aggressive towards me, the young person appears sorry for doing it -0.443 22 They appear emotionally conflicted 0.650 21 They appear to be not in control of themselves 0.517 18 They appear anxious, frightened, or scared 0.427 8 The young person is quick to become very angry 0.422 6 I can predict when the young person is likely to respond with violence or aggression 0.397 aggression towards others (r = 0.68). The model predicting reactive aggression towards others was statistically significantly (F (6, 85) = 12.28, p < 0.001) and accounted for 55% of the variance in reactive aggression towards others; Reactive CPV was significantly associated with reactive aggression towards others, ß = 0.29, t = 2.61, p = 0.011. The model predicting proactive aggression had a mildly heteroscedastic distribution of standardised residuals, however this did not impact the results. The model was statistically significantly (F (6, 85) = 23.82, p < 0.001) and accounted for 63% of the variance in reactive aggression towards others. Proactive CPV was associated with high proactive aggression towards others (ß = 0.57, t = 5.52, p < 0.001), whereas reactive CPV was associated with lower proactive aggression towards others (ß = -0.24, t = -2.35, p = 0.021). The full model is presented in Table 4. The final model explored the association between the function of CPV and the severity of CPV. Three potential outliers were detected with standardised residuals of two standard deviations above the average. Two of these cases were removed as they had a significant impact on the results. Inspection of a plot of standardised residuals versus standardised predicted values revealed a mildly heteroscedastic distribution, which was corrected using a square root transformation. The model was statistically significant (F (5, 98) = 30.14, p < 0.001) and accounted for 61% of the variance in the severity of CPV. All CPV functions, as well as age, were statistically significant, with proactive having the strongest association, ß = 0.57 t = 5.84, p < 0.001.

Discussion
The aim of the current study was to develop and validate the Child-to-Parent Violence Functions Scale (CPV-F) in a sample of caregivers who met the criteria for experiencing abuse from their young person.

Structure of the CPV-F
Three discriminant, but related factors emerged: Reactive, Affective, and Proactive functions of CPV. Reactive CPV items reflect an aggressive or defensive response to conflict, threat, and punishment; Affective CPV captures aggression that is primarily due to internal frustration, anxiety, or conflicting emotion (consistent with Blair, 2013;Smeets et al., 2017); and Proactive CPV represents strategic, instrumental, and callous acts of aggression. Consistent with other areas of aggression, these factors were highly correlated, particularly Reactive and Proactive CPV. The Affective factor shared a comparatively smaller relationship with the other factors. It may be that the Affective factor captures the more unique aspect of aggression which is represented elsewhere in a Reactive factor (i.e., a composite measure of affective and reactive functions). In exploratory analyses which were not reported (see supplementary Table 1), Affective CPV was not significantly associated with Proactive CPV; the correlation here is instead an artifact of the relationship between Affective and Reactive CPV. Some young people are 'reactive only' (Euler et al., 2017;Smeets et al., 2017) and the current study suggests that aggression in this group may be more appropriately described as a result of internal frustration rather than provocation (i.e., Affective, not Reactive). Although, it is noted that this aggression would still require some form of 'trigger', which could be conflated with provocation. However, the critical difference being that the frustrated, anxious, or emotional state which drives the aggression was likely present before the trigger in Affective CPV, rather than being produced following the trigger or provocation in Reactive CPV. The presence of pre-existing affect may be why the predictability of Affective and Reactive CPV vary. Caregivers who experience Affective CPV report being able to predict acts of aggression, whereas those who experience Reactive CPV report aggression when they are 'not expecting it'. This is counter-intuitive given that there is often an external precursor to Reactive CPV (e.g., punishment), which the caregiver controls and would learn to expect an aggressive response from. However, it may be the young person is sensitive to and reacting to more perceived transgressions or intrusions from the caregiver, unrealised by the caregiver, that it becomes difficult to anticipate or identify the trigger. Indeed, much of the provocation in reactive aggression depends on the aggressor's interpretation of the event (Bailey & Ostrov, 2008;Gagnon & Rochat, 2017), which would reduce how predictable the aggression is. Whereas with Affective CPV, the pre-existing mood of the young person is important and may provide an indication as to when aggression is likely, or unlikely.
Affective CPV empirically derived from the CPV-F appears to be different to that recently theorised elsewhere.
Following a systematic review, Ibabe (2020) offered four typologies of CPV: Offensive (i.e., proactive and controlling), defensive (i.e., in direct response to victimisation), affective (e.g., anger and in response to threat), and situational (i.e., low severity conflict). Ibabe's Affective CPV is captured in our Reactive CPV, as is defensive CPV, which would be challenging to measure reliably using caregiverreport, due to under-reporting. For example, in the current study the item "I use physical punishments (e.g. slapping or hitting) …" received little endorsement and consequently did not factorise, despite corporal punishment being common in families experiencing CPV (Del Hoyo-Bilbao et al., 2018, 2019. The CPV-F navigates this challenge through careful wording of alternate items which mitigate perceptions of blame (e.g., "The young person gets angry when they perceive me as being threatening, aggressive or violent towards them"). Affective CPV, as proposed by Calvete and Orue (2016), also includes consideration of anger, but the items better reflect attitudes, or resentment from the young person toward the parent (e.g., "they treat me like a little child" and "I feel misunderstood"). It could be that these are some of the reasons which contribute to or precede the internalising problems captured by reactive CPV in the CPV-F, however these are not directly comparable.
The existence of the Affective factor differentiates the 3-factor CPV-F from the 2-factor CPV-Q Reasons subscale. However, this 3-factor solution may only emerge in clinical samples (Smeets et al., 2017). While the current sample was recruited from the community, the level of abuse reported is of clinical significance. For less severe abuse (i.e., a low frequency of verbal violence), where adjustment issues are more mild, this factor may not emerge. Indeed, Affective aggression may be primarily related to internalising problems (Smeets et al., 2017) associated with more severe violence (Bartels et al., 2018), and the majority of CPV research is conducted on samples characterised by low severity of violence.
The rates of instrumental, or proactive CPV, were not consistent with rates measured using the CPV-Q on community samples. Contreras et al. (2019) found that instrumental reasons for aggression (some which overlapped with items on our Proactive subscale), were the most common reasons for CPV. However, in the current study, the Proactive function was reported with the least frequency, on average (M = 1.50); Affective CPV was the most frequent, on average (M = 2.37). These rates better reflect general aggression literature, where proactive aggressions are a rarer occurrence (e.g., Connor et al., 2003;Moore et al., 2019;Rieffe et al., 2016). This discrepancy may be due to age differences between validation samples. Proactive aggression is likely learned over time (Baker et al., 2008;Polman et al., 2007) and indeed, higher Proactive CPV scores were more common in older young persons in the current sample (though this should be interpreted with caution as the subgroups were small). Our sample had a wide age range (5-24); the younger cohort may have thereby reduced the sample average for Proactive CPV. Investigations using the CPV-Q have been primarily undertaken on young people within an age range restricted to adolescence.

Concurrent Validity
The CPV-F demonstrated good concurrent validity through comparisons to the PRPA. Proactive CPV was the only significant positive association with proactive aggression towards peers and siblings. Further, reactive CPV was associated with reactive aggression against others. This not only demonstrates the concurrent validity of the CPV-F, but also shows that the function of a young person's violence is likely consistent across settings and between targets, thus presenting evidence against a generalist and specialist model of CPV. It is more likely that CPV, when properly operationalised, co-occurs with a more generalised pattern of delinquency, as found in forensic cases . Notably though, Affective CPV remained a distinct function of aggression and was not associated with reactive or proactive aggression against others. According to the theory developed by Kuay et al. (2017), Reactive CPV was anticipated to characterise young people who were aggressive towards only their parents. We suggest that Affective CPV, rather than Reactive CPV, could identify this group, given the lack of associations with violence towards others, found in our sample. However, to substantiate this point, a person-based analysis would be required to determine if there are some young people who only use Affective CPV.

Predictive Validity
It was anticipated that Proactive CPV would be positively associated with high CU traits, consistent with past research in general adolescent violence. In line with this, we found that CPV characterised with a proactive function is far more likely to be used by young people with high CU traits. This suggests that much of the facilitation for severe, proactive CPV may be temperamental and attributable to callousness and unemotionality, similar to general adolescent violence. Indeed, aspects of proactive CPV (e.g., the young person enjoying the act of violence) necessitate a disregard for the target. Of note, the rates of high CU traits in our sample were well above community norms, and better align with prevalence in populations of young people with conduct disorder (Herpers et al., 2012). Almost half the young people (48%) were classified as having high levels of CU traits (Using a cut-off score of 30 on the 22-item ICU; Docherty et al., 2017). Child-to-Parent Violence may be a severe form of child/adolescent aggression in and of itself, and an early indicator for significant maladjustment. However, there is discordance between the prevalence of this risk factor (within the current study) and the attention received to date; only a handful of studies have investigated CPV and CU traits (Cortina & Martín, 2020;Kuay et al., 2016). Most recently, Del Hoyo-Bilbao et al. (2021) demonstrated that, while the impact of psychopathic traits on CPV was small, CU traits played an important moderating role on the impact of grandiose-manipulative traits on physical CPV, strengthening the association when levels of CU traits were high. Further, when CU traits were low, the relationship between impulsivity and physical CPV became non-significant. As such, future research on CU traits and CPV should also consider the role of adjunct psychopathic traits.
Due to these temperamental differences, Proactive CPV should also facilitate more severe abuse. We found that, whilst all functions were associated with increasing severity of abuse, proactive CPV facilitated the steepest rise. This finding supports previous research on general adolescent aggression (Crapanzano et al., 2010;McCloud, 2017) and suggests that proactive aggression may be universally indicative of severe aggression, regardless of the target. This is particularly noteworthy within the parent-child relationship, as proactive aggression is favoured against targets perceived as less powerful, which violates traditional family hierarchy. Thus, it may be that in families experiencing proactive CPV, role-reversal or parentification has occurred. The current literature has only briefly explored power imbalances and found that role-reversal appears to become more prevalent as the severity of cases increases from community categorisation/average to forensic categorisation/average (Loinaz & de Sousa, 2019;Peek et al., 1985); this may be driven by concurrent increases in proactive CPV.

Reliability
Reliability of the scale was adequate overall. The reliability of the Affective CPV sub-scale was questionable (0.62), albeit acceptable for exploratory research (Hair et al., 2009). In its current structure, the factor represents different forms of internal frustration (e.g., anxiety, anger, emotional conflict); this diversity may have contributed to lower internal consistency of the sub-scale. Nonetheless, the factor loadings were strong, and the factor is discriminant from Reactive CPV, both internally within the scale, as well as in its associations with other variables in the study. Future research using the CPV-F should continue to monitor and report the reliability of the Affective subscale; it may be more appropriate to break the factor down further, into two subscales: internalised fear, and internalised anger.

Strengths, Limitations, and Implications
A strength of the current study was the measurement of abuse and strict inclusion criteria. All participants in the current study were experiencing ongoing and/or severe violence, which was determined through empirical measurement validated for the Australian community (Simmons et al., 2019). Indeed, a problem within the CPV literature is the operationalisation of CPV, which often includes low rates of violence, such as single or highly infrequent occurrences of verbal or physical aggression (e.g., Ghanizadeh & Jafari, 2010;Lyons et al., 2015;Margolin & Baucom, 2014;Pagani et al., 2009). This leads to inflated prevalence estimates , as well as conclusions about CPV being made from samples characterised by low levels of aggression. This problem has also contributed to the significant heterogeneity in findings between CPV studies . It is essential that 'one off', or situational (Ibabe, 2020), non-problematic incidents of conflict (particularly verbal conflict) are not used to represent CPV, in order to protect the clinical utility of findings for treatment seeking families. In the current study, we ensured participants were experiencing recent, repeated, and substantial violence (i.e., abuse). As a result, our sample was smaller than other studies, but is representative of families experiencing CPV who are more likely to present for treatment.
However, it is important to consider that the sample size, while acceptable, was small for factor analysis (Costello & Osborne, 2005;MacCallum et al., 1999). This was due to our strict screening process to ensure participants were experiencing serious and repeated abuse, rather than one-off instances of aggression. This limits our ability to generalize our findings to the broader population of families experiencing CPV. There is also a higher likelihood of error within factor loadings for smaller studies. Though this increase in error is small (Costello & Osborne, 2005), future research using the CPV-F should run and report confirmatory models to further confirm the factor structure.
The current study was also limited in diversity of male and female caregivers. Single mothers are over-represented in the experience of CPV (Holt, 2016). In families where the father is still physically present, practitioner reports suggest that these fathers may remain emotionally absent or absent from parenting responsibilities (Calvete et al., 2014). Fathers may primarily experience a reactive form of abuse, when the young person is provoked (Simmons, 2018) and uninhibited (Pagani et al., 2009). Further, proactive aggressions are more likely enacted toward a victim perceived as weaker than the aggressor (Hubbard et al., 2001). This was preliminarily supported by case studies where father victims did not report experiencing the controlling abuse which mothers reported (Daly & Wade, 2015). Therefore, the lack of fathers in the current sample may have led to an over-representation of Proactive CPV. Notwithstanding, the current study draws attention to the need to consider the function of CPV in future CPV research and provides a tool to do so in parent samples. Future research using the CPV-F should specifically target fathers during recruitment, especially in clinical settings, as this is demonstrated to increase their involvement in family research (Davison et al., 2017;Macfadyen et al., 2011).
The functions identified by the CPV-F have utility to services providing intervention to families experiencing CPV, as well as researchers in the area. There is clinical and empirical demand for interventions which can adapt to the individual needs of families experiencing CPV (Holt & Shon, 2016). In one recent study, 83% of young people with a CPV-related charge had engaged with, but been unsuccessful in a previous intervention (Loinaz & de Sousa, 2019). Proactive and reactive aggression have unique processes and environments associated with their use (Hubbard et al., 2010), which can form the basis for individualised (McAdams, 2002), responsive, and thus more effective treatment (Andrews et al., 2011). A review by Curtis et al. (2019) has previously provided guidance on how these interventions could be adapted. Alongside the tailoring of intervention, the ability for service providers to identify the function of CPV will also aide in risk-appropriate delivery of intervention, and the identification of severe cases (which proactive aggression is an indicator of; Smeets et al., 2017). For researchers, the function of aggression is demonstrated to impact the relevance of risk factors. For example, within the area of CPV, there is emerging evidence to suggest that proactive and reactive CPV are associated with unique social-cognitive process (Contreras et al., 2020b). Thus, future research should consider the impact of the function of CPV, particularly that of Affective CPV, which is previously unexplored, in order to guide adaption to intervention. The parent-report nature of the CPV-F also allows researchers to explore parent variables (e.g., parent stress and trauma) alongside the function of CPV they are experiencing; parent samples have been largely under-utilised to date.

Conflict of Interest
The authors declare that they have no conflict of interest.
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