Associations between parenting behaviour and paranoia were first tested in the National Comorbidity Survey Replication Adolescent Supplement (NCS-A)  and then in a new survey conducted to assess the key variables in greater depth. The NCS-A survey was administered using computer assisted, face-to-face, individual interview by professional interviewers employed by the Survey Research Centre. The interview schedule was based on the World Health Organisation Composite International Diagnostic Interview (WMH-CIDI). Merikangas et al. report further details of the adaptions to measures in the NCS-A . A hard copy of the instrument is posted at www.hcp.med.harvard.edu.ncs. The new survey was administered via Qualtrics, an online questionnaire platform.
The NCS-A sample included 10,148 adolescents aged 13–17 years old. 9244 adolescent students were selected from a representative sample of 320 schools in the same nationally representative sample as the National Comorbidity Survey-Replication (NCS-R) (response rate 74.7%). The remaining 904 participants were from the same households of those that took part in the National Comorbidity Survey-Replication (response rate 85.9%). The mean age was 15.18 years (SD = 1.51) and 48.9% (n = 4962) of the sample were male, 51.1% (n = 5186) female.
Oxfordshire participant group
The second participant group consisted of 1231 adults (aged 18 or over). Participants took part in the survey as part of the screening process for an experimental study that was advertised via social media adverts in the region of Oxfordshire, UK. The mean age of this survey group was 41.54 years (SD = 15.95). Data on participant gender were not collected for the first 207 participants. Of the remaining 1024 participants, 23.7% (n = 243) were male and 76.3% (n = 781) female. It is typical for online surveys to receive a considerably higher response rate from women [37, 38]
Participants were asked to respond to the following statement with ‘true’, ‘false’, or ‘do not know’: ‘People often make fun of me behind my back’. This item has previously been used as a brief measure of paranoia . A correlation difference test supported the internal validity of the measure by showing that this single-item measure of paranoia (n = 857) had a significantly higher correlation with a 16-item measure of paranoia (the Green et al. Paranoid Thoughts Scale-Part B, Green et al., 2008)  (r = 0.56), than with a measure anxiety (r = 0.38), z = 15.00, p < 0.0001.
Participants were asked to respond to the following statements with ‘a lot’, ‘some’, ‘a little’, or ‘not at all’ for both mother and father figures separately: ‘How much did he/she really care about you?’; ‘How overprotective was he/she?’. Participants were asked to respond to the following lists and statements with ‘often’, ‘sometimes’, ‘not very often’, or ‘never’ for both mother and father figures separately: ‘When you were growing up, how often did he/she do any of these things to you?’: ‘insulted or swore, shouted, yelled or screamed, threatened to hit’ [verbal abuse (List A)]; ‘pushed, grabbed or shoved, threw something, slapped or hit’ [physical abuse (List B)]; ‘kicked, bit or hit with a fist, beat up, choked, burned or scalded, threatened with a knife or gun’ [severe physical abuse (List C)].
Oxfordshire participant group
The Oxfordshire participant group completed the same measures of paranoia and parental behaviour described for the NSC-A dataset, as well as the following measures:
Participants completed the Green et al. Paranoid Thoughts Scale—Part B (GPTS-B) . This is a 16-item scale assessing ideas of persecution over the past month such as ‘I was convinced there was a conspiracy against me’ and ‘I was sure someone wanted to hurt me’ on a 1–5 scale (1 = not at all, 5 = totally). Scores can range from 16 to 80; higher scores reflect greater paranoia. The scale is well validated for use in both clinical and non-clinical samples  and has strong concurrent validity with paranoia severity as assessed by clinical interviews and by controlled virtual reality tests [42, 43]. Using item response theory analysis with over 10,000 individuals, the GPTS-B has been shown to demonstrate high reliability (a > 0.95) across both mild and severe ends of the paranoia spectrum . Test–retest reliability has also been shown to be good, with an intra-class correlation coefficient of 0.81 .
The Measure of Parenting Style (MOPS)  was used. This contains 15 items measuring specific maternal parenting behaviours and the same 15 items measuring paternal parenting behaviours. It was developed to overcome shortcomings of the Parental Bond Instrument  and assesses reported parental indifference, abuse, and over-control separately for mothers and fathers. Higher scores reflect higher reported levels of each behavior. Alpha coefficients of internal consistency for each of the six subscales range from 0.76 to 0.93 .
Although two of the subscales were named differently from the parenting questions included in the NCS-A dataset (indifference vs. amount of care, and over-control vs. over-protection), they were taken in our study to be measuring the same constructs. This was justified upon Parker et al.’s descriptions of both over-protection and care described above . The abuse items in the MOPS were similar to those in the NCS-A dataset in separately measuring both physical and verbal abuse.
The self-compassion scale-short form (SCS-SF) was used . The scale consists of 12 items asking about how respondents typically act towards themselves in difficult times, rated on a Likert scale of one (almost never) to five (almost always), meaning higher scores reflect higher levels of self-compassion. There are six subscales, but use of a total score is recommended when using the short form. The SCS-SF demonstrates good internal consistency (Cronbach’s α > 0.85 and a near-perfect correlation with the long form of the scale when using total scores (r > 0.96) .
Compassion for others
Participants were given the Compassion Scale , a 24-item scale measuring how respondents typically act towards others. As with the SCS-SF, items are rated on a Likert scale of one (almost never) to five (almost always) and there are six subscales, but a total score can also be used. Higher scores reflect higher levels of compassion for others. The scale demonstrates good internal consistency (Cronbach’s α = 0.9) .
Anxiety and depression
The Patient Health Questionnaire-4 (PHQ-4)  is a brief four-item scale for anxiety and depression that has been well validated for detection of anxiety and depression in clinical samples . Two items measure anxiety over the past two weeks and two measure depression over the past two weeks. Higher scores reflect greater anxiety and depression. Internal consistency for the scale is good (Cronbach’s α = 0.85) . The two item measure of anxiety used has shown high sensitivity for identifying generalised anxiety (88%), panic (76%), and social anxiety (70%), as well as moderate sensitivity for PTSD (59%) .
The Rosenberg Self-Esteem Scale  is a highly used ten-item measure of global self-worth that measures positive and negative feelings about the self. Items are answered using a four-point Likert scale ranging from strongly agree to strongly disagree. Scores range from 10 to 30. Five items are reversed scored so that higher total scores indicate higher self-esteem.
The NCS-A data were analysed using the Statistical Package for the Social Sciences . The data were weighted to adjust for within-household differential probabilities of respondent selection. Details of the rationale and process of weighting have previously been reported [35, 53]. Logistic regressions were used to test the associations between the assessments of parental behaviour and paranoia. Standard mediation analyses were not conducted due to the cross-sectional nature of the data . Gender was included as a co-variate in all analyses. All tests were two-tailed. The primary analysis was conducted separately for mother and father figures, given that interactions between them would be based on small amounts of data for key categories.
First, identical logistic regressions as above were conducted using the same measures of parenting and paranoia as were included in the NSC-A dataset. Second, simple regressions were conducted for the more in-depth measures of parenting and paranoia completed by the Oxfordshire participant group.
Network analysis with the measures from the Oxfordshire survey was conducted in R, version 3.6.1 . A network modelling approach was used to estimate the partial correlations between paranoia and the other measures. In network analysis, variables are represented by nodes. Two nodes may be connected by an edge. Edges represent an association between two variables after controlling for all other variables included in the network, i.e., a partial correlation. The absence of an edge between two variables indicates that the partial correlation is zero after controlling for all other variables, known as conditional independence. Associations are visualised in a network where the thickness and saturation of the edge colour corresponds to the strength of the relationship .
Using the package qgraph, a Gaussian graphical model was fitted . A regularisation technique with the Least Absolute Shrinkage and Selection Operator (LASSO) was used to overcome any potential sampling variation and limit the estimation of false positives . The LASSO regularisation shrinks estimates by employing a penalty that limits the sum of the partial correlation coefficients . The degree of regularisation is controlled by a tuning parameter, which is selected to optimise the model fit by minimising the Extended Bayesian Information Criterion (EBIC) . The EBIC hyperparameter is set between 0 and 0.5, with a lower parameter resulting in more potential false edges being retained, and a higher parameter potentially omitting true edges from the network . A hyperparameter of 0.3 was therefore chosen. Using the package bootnet, a non-parametric bootstrap with 5000 interactions was conducted, to construct 95% confidence intervals for each edge . Due to the method of regularisation edge weights are biased towards zero. Consequently, reported confidence intervals cannot be interpreted as a significance test against zero .
Two separate network models were constructed to show the shortest path between paranoia and every other variable, and between the parenting variable found to have the strongest edge with paranoia and every other variable using Dijkstra’s algorithm . The shortest path represents the quickest route for an interaction to occur between two variables, calculated using the strength of edge weights along each potential route. In this way, even though two nodes may share a direct path, an indirect route via an intermediary node may consist of stronger associations and therefore be a quicker route. Redundant edges are then supressed. Such a network is helpful for highlighting likely mediation pathways.