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### Mathematics in DCLG: homelessness

Andrew Presland

Statistician, Neighbourhoods Analysis Division, DCLG

DCLG collects data from 326 English local authorities on three types of

homelessness:

Numbers of people who apply to local authorities for assistance under the Housing and Homelessness Acts, the demographics of those who are found to be eligible and the number of those in temporary accommodation.

Numbers and estimates of rough sleepers by local authority

Numbers of prevention and relief activities carried out by local authorities

Data collected by DCLG

Statutory homelessness

When people apply for assistance, the local authority bases their decisions on a number of criteria:

- Eligible for assistance
- Homeless or threatened with homelessness within 28 days
- Priority Need
- Intentionality
- Local connection

The P1E form

- The P1E form is large and detailed
- Over five hundred data items per local authority each quarter
- But over 99% of local authorities provide figures, probably because they have them on their systems anyway.

The latest figures on from the Statutory Homelessness publication showed that 29,100 decisions on eligibility for assistance were made between 1 October and 31 December 2012:

- 47 per cent were accepted as owed a main homelessness duty (these are known as \'homelessness acceptances\');
- 28 per cent were found not to be homeless;
- 17 per cent were found to be homeless but not in priority need
- 8 per cent were found to be intentionally homeless and in priority need.

Priority Need groups

- Households with dependent children 51-63%
- Household member pregnant 10-12%
- Old age 1-4%
- Physical disability 5-7%
- Mental illness 7-9%
- Young person 3-9%
- Domestic violence 3-6%
- Other 5-8%
- Homeless in an emergency 0-1%

Characteristics of households accepted as homeless

- Age of applicant:
- 25-44 year olds 47%
- 16-24 year olds 41%
- Type of household:
- Lone female parents with dependent children 43-47%
- Couples with dependent children 18-20%.
- 1 person households 30% in 06/07 down to 23% in 11/12.
- More single male households than single female households.

Comparing trends in homelessness acceptances (flows) and temporary accommodation (stocks)

Latest figures

- The Autumn 2012 total of rough sleeping counts and estimates in England was 2,309.
- This is up 128 (6%) from the Autumn 2011 total of 2,181.
- All 326 local housing authorities in England provided a figure. The total comprises counts provided by 43 local authorities and estimates provided by 283 local authorities.
- London had 557 rough sleepers, which accounted for 24% of the national figure.

Using maths to investigate homelessness

- Relatively little use of high-powered statistical methods, let alone maths, when
- working with homelessness statistics.
- Limited largely to making estimates for non-responding local authorities, and seasonal adjustment of some figures.
- Also starting to see if there\'s scope for developing a regression or econometric model for predicting the number of homelessness acceptances
- Even less use of mathematics:
- Only clear example is mathematical formulae developed in the 1990s to model the expected impact of restricting statutory homeless households to no more than twelve months in temporary accommodation.

Modelling stocks and flows (2)

- Data collected on the P1E are a mixture of stocks and flows:
- Flows into and out of being subject to the homelessness duty applying
- Stocks of households in temporary accommodation at a given snapshot date
- Broken down into quite a lot of detail.
- But complications too:

i) Some households are \'homeless at home‘, rather than in temporary accommodation.

ii) Temporary accommodation figures include some categories of household that haven\'t been accepted as homeless (e.g. if pending review, or intentionally homeless) – and some of these can’t be separately quantified.

- Scope to use mathematical methods to give a clearer picture – e.g.
- i) Understanding what\'s already happening, including recent policy changes?
- ii) Modelling the impact of possible future policy changes?
- iii) Different models for different geographical areas, or types of household or temporary accommodation etc?

Modelling stocks and flows (3)

A previous attempt to set out the stocks and flows implicit in P1E data

Some other possible mathematical applications of statutory homelessness statistics

- 1. Looking at the characteristics of homeless households – e.g. mental health issues;
- drugs/alcohol; unemployed
- To what extent are these characteristics caused by being homeless?
- Or is it more the case that people with these characteristics are more likely to become homeless in the first place?
- Can mathematical methods be used to explore this, or is proving causality more naturally the territory of statisticians or economists?
- Can mathematical models be used to forecast or predict numbers of homelessness acceptances, or numbers in temporary accommodation, e.g. using…
- time series?
- differential equations?
- Markov matrices for predictions?

Possible mathematical applications of other homelessness statistics

- 1. Homelessness prevention and relief cases
- Investigating the relationship with numbers of statutory homelessness acceptances
- Does successful prevention activity take place more frequently in areas of high statutory homelessness (e.g. where tackling homelessness is given a higher policy priority)
- Or is it more common in areas of low statutory homelessness (e.g. because the prevention work is successful)?.
- 2. Rough Sleeper count
- Can local authorities’ basic annual count of people be enhanced using other data, such as the day-by-day detailed monitoring that voluntary sector groups do across London?
- “Hidden homeless” (e.g. ‘sofa surfers, adult children living reluctantly with parents)
- No official data, but historic estimates have been made by VCS groups.
- York University has recently developed estimates using related data sources, such as English Housing Survey data (overcrowding).
- Could mathematical methods be used to take things further?

Over to you…

- Does anything need clarifying?

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