Prison population: social care needs

Annex – Technical methodological detail

Methodology 1: Applying current state intervention levels

The first approach is a four-step methodology to estimate the social care needs of prison population through modelling the social care needs of the non-prison Scottish population.

Step 1: Estimate the probability of the Scottish community having social care needs

The first step of the current methodology is the estimation of the probability of having social care needs. The Scottish Household Survey 2017 was used as it is a dataset that includes people with and without social care needs. The following logit model was estimated:

 (1)

where: 

• i indexes the individual,
• has_social_care_needs is a dummy variable that takes the value of 0 if the individual does not have social care needs and 1 if they do. The dummy variable was constructed using the "rg5b" variable from the survey, which asks participants whether their physical or mental health condition or illness lasting or expected to last 12 months or more (conditional that they are in this situation) reduces their ability to carry out daily activities. People replying "yes, a lot" were classified as people with social care needs, and people replying "yes, a little" or "not at all" were recorded as not having social care needs,
• female is a dummy variable with 1 if the individual is female and 0 otherwise,
• age is the age of the individual as a continuous variable,
• deprivation_quintile is a categorical variable whose values range from 1, for individuals who come from the 1^st SIMD quintile (most deprived areas), to 5 for those who come from the 5^th SIMD quintile (the least deprived areas),
• γ is the interaction of age and deprivation_quintile, and
• represents a random error term.

After estimating equation (1), the probability of having social care needs was predicted for each individual in the sample.

Step 2: Calibrate to social care administrative data

The percentage of people who have social care needs in the Scottish Household Survey 2017, based on the "has_social_care_needs" dummy variable that was constructed in Step 1, does not match the social care administrative statistics. In particular, around 13% have social care needs in the Scottish Household survey 2017, while official administrative data indicates that 4% of the Scottish population receive social care and support from Local Authorities.  

Therefore, the predictions from Step 1 were calibrated to match the population frequencies in the administrative data. First, the sample from the Scottish Household Survey was classified into age groups: <30, 30-39, 40-49, 50-59, 60-59, 70-79, 80+. The predicted probabilities of having social care needs as estimated in Step 1 were sorted for each age bracket and gender. The next step included the construction of a new dummy for having social care needs, which was set to 1 for the top x% of the sorted probabilities within each gender and age group, where x% represents the proportion requiring social care support based on Scottish administrative data, and 0 otherwise. 

Step 3: Estimate with the revised social care dummy

This step included the estimation of a model similar to the one constructed in Step 1, using the new social care needs dummy constructed in Step 2 as the dependent variable.

  (2)

where:

• i indexes the individual,
• has_social_care_needs is the dummy constructed in Step 2, where 1 defines the individual with social care needs, and 0 otherwise,
• female is a dummy variable with 1 if the individual is female and 0 otherwise,
• agegroup is the categorical variable of age, classifying the sample into the following age groups: <30, 30-39, 40-49, 50-59, 60-69, 70-79, 80+, and
• deprivation is a dummy variable that takes 1 if the individual comes from the bottom 1^st or 2^nd SIMD quintile, and 0 otherwise. 

The model (2) was used in the next step to create a probability estimate of social care needs for each person in Scottish prisons.

Step 4: Estimate social care needs of Scottish prison population

In this step, the model (2) from Step 3 was applied to the Scottish prison population. First, the model was used for the non-prison population, and then, the results were extrapolated to the prison population, by predicting the probability of having social care needs for the whole sample, i.e. prison and non-prison population.

Methodology 2: Self-reporting social care needs

Similar to Methodology 1, this approach is based on extrapolating estimates of social care needs of the Scottish non-prison population to the Scottish prison population. The main difference between the two approaches is that Methodology 2 is based on self-reporting of social care needs rather than calibrating to administrative data of individuals receiving social care interventions.

As in Methodology 1, the probabilities of having social care needs were estimated for the non-prison population, and then, the results were extrapolated to the prison population. In this approach, two different specifications were used to predict the probability of people in custody having social care needs. 

Specification A:

The first specification is similar to the model used in the 4^th step of Methodology 1. The independent variables used for estimating the logit model were the same as before, but the dependent variable was varied to be based on self-reporting of needs in the Scottish Household Survey:

  (3)

Specification B:

In this specification, the deprivation dummy was excluded:

  (4)

Specification C: 

In this specification, the deprivation dummy was excluded but the premature ageing of the prison population was taken into account. In particular, adopting the 10 year-differential ageing between prison and non-prison population, the age of the prison population is shifted by a decade to better match the age of the non-prison population.

 (5)

where:

• differential_ageing is the categorical variable of age for the non-prison population, classifying them into the following age groups: <30, 30-39, 40-49, 50-59, 60-69, 70-79, 80+. The age of the prison population has been adjusted in the following way: people in custody whose age group is 16-20 has remained in the "<30 age group; people whose age group is 21-29 years old have been moved to the 30-39 age group; people whose age group is 30-39 have been moved to the 40-49 age group, and so on.