Appendix C. Technical detail on quantitative modelling
Logistic regression was used to estimate the mental health needs of the prison population through modelling the mental health needs of the non-prison Scottish population. This occurred in a two-step process.
Step 1: The first step in this process was the estimation of the likelihood of having a mental health need based on individual demographics. The Scottish Health Survey 2019 was used as it includes a nationally representative sample of individuals, both with and without mental health needs. Cases corresponding to individuals aged 16 years or older were retained for analysis. The following regression model was estimated using maximum likelihood estimation:
has mental health need
= β0 + β1femalei + β2ethnic minorityi + β3agei + β4deprivationi
- i represents each individual in the dataset,
- has_mental_health_need is a nominal dummy variable which takes the value of 0 if the individual does not have a mental health need and 1 if they do. A dummy variable was created for each of the five mental health needs modelled. The value of 1 was used according to the following criteria: the individual (1) reported having a long-term mental health condition; (2) reported a history of deliberate self-harm or attempted suicide; (3) scored 8 or higher on the AUDIT indicating hazardous or harmful drinking; (4) reported two or more symptoms of depression in the previous week on the CIS-R depression section; (5) reported two or more symptoms of anxiety in the previous week on the CIS-R anxiety section,
- female is a nominal dummy variable which takes the value of 1 if the individual is female and 0 if the individual is male,
- ethnic_minority is a nominal dummy variable which takes on the value of 0 if the individual reported being white and 1 if the individual reported being from a ethnic minority group.
- age is an ordinal dummy variable indicating the individuals age in years according to specified bands: 16-20; 21-30; 31-40; 41-50; 51-60; 61-70; and over 70.
- deprivation is a dummy variable which takes on the value of 1 if the individual's SIMD is from the two most deprived quintiles, and a value of 0 if not.
- εi represents the error term corresponding to variance unaccounted for by the above predictor terms.
After estimating the equation the probability of having each of the five mental health needs was predicted for each individual in the SHeS 2019 sample.
Step 2: In the second step, the individual likelihood estimates derived from the SHeS 2019 sample were applied to every individual in Scotland's prison population, recreated using the PR2 extract. While the PR2 system does not hold information on the SIMD of the communities from which individuals come into prison, people in prison in Scotland are most likely to come from the bottom two SIMD quintiles (Scottish Public Health Observatory, 2010). Therefore in applying the likelihood estimates to the prison population, likelihood estimates corresponding to being in the bottom two SIMD quintiles were applied to the PR2 extracts.
After deriving probabilities for every individual based on age, gender, ethnicity, probabilities were then summed across different prison population subgroups to yield the proportion of the prison population by gender, age group, legal status as well as the prison population as a whole who are likely to have a mental health need.
Likelihood Ratio Chi-Square (x2) was significant for each model indicating improvement over the null model in each case.
- Long-term mental health condition: x2(9) = 178.35, p <.001
- History of deliberate self-harm or suicide attempt: x2(9) = 54.24, p <.001
- Alcohol use disorder: x2(9) = 309.57, p <.001
- Symptoms of anxiety: x2(9) = 27.98, p = .001
- Symptoms of depression: x2(9) = 31.178, p <.001
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