Homelessness in the UK: who is most at risk?

Figures & data

Table 1. Logistic regression model for adults reporting having ever experienced homelessness, Scotland 2001–2007 and 2010 (Scottish Household Survey).

Description	Level	Block	Coeff. B	Sig.	Exp(B)
Aged under 25	INDIV	DEM	−0.349	0.000	0.71
Aged 25–34	INDIV	DEM	−0.077	0.064	0.93
Aged 50–64	INDIV	DEM	−0.550	0.000	0.58
Aged 65+	INDIV	DEM	−1.610	0.000	0.20
Single person hhd <65	INDIV	DEM	0.265	0.000	1.30
Lone parent hhd	INDIV	DEM	0.696	0.000	2.00
Multi adult hhd	INDIV	DEM	−0.178	0.009	0.84
Sick/disabled indiv	INDIV	DEM	0.404	0.000	1.50
Income-related benefits	INDIV	POV	0.508	0.000	1.66
Financial difficulties (1)	INDIV	POV	0.687	0.000	1.99
Low income % popn (2)	SA	POV	0.015	0.000	1.02
No qualifications	INDIV	LM	0.343	0.000	1.41
Occup routine/service	INDIV	LM	0.174	0.000	1.19
Occup unskilled/unclassif	INDIV	LM	0.174	0.000	1.19
Household with 2+workers	INDIV	LM	−0.418	0.000	0.66
Hhd unemployment rate	INDIV	LM	0.476	0.000	1.61
Access index (3)	SA	LM(A)	0.003	0.003	1.00
Unemployment rate %	LA	LM(A)	−0.140	0.000	0.87
Social renter	INDIV	HSG	1.106	0.000	3.02
Private renter	INDIV	HSG	0.797	0.000	2.22
Number of rooms	INDIV	HSG	−0.224	0.000	0.80
Apartment dwelling	INDIV	HSG	0.222	0.006	1.25
Social renting %	LA	HSG(A)	0.012	0.000	1.01
Private renting %	SA	HSG(A)	−0.625	0.013	0.54
Net need aff hsg % hhd (4)	LA	HSG(A)	0.102	0.001	1.11
Constant			−2.528	0.000	0.08
Model summary			R^2	R^2	χ^2
		−2 L L	Cox/Snell	Nagelkerke	(25 df)
		32,076.9	.078	.236	8118.9

Notes: (1) Household has some financial difficulties or is in deep financial trouble: (2) Scottish Indices of Multiple Deprivation (SIMD) ‘Low Income Score’, based on % of population claiming income-related benefits; (3) SIMD ‘Access to Services Score’, based on time to reach selected services (a ruralitymeasure); (4) Annual need for affordable housing, based on house prices, modelled incomes and demography, less social sector lettings supply.

The following variables were tested but omitted as insignificant at the individual/household level: female; and several indicators of affluence; ethnicity; pensioner household types; household size; overcrowded households. Excluded area factors include: ‘city’ dummy; population sparsity; employment rates; median earnings; household incomes and house price level or change; house price: income ratios; vacancies and social relet rates; as well as certain ‘SIMD’ neighbourhood indicators include the ‘education’ and ‘health’ scores. (Some area variables were excluded because of multicollinearity problems and because they clearly overlapped with other included variables.).

A cut-off of 0.225 on the predicted homelessness probability value yields a number of predicted positives close to the observed total (5200), with correct positive predictions then representing 30% of actual homeless number.

Table 2. Comparison of performance of models including blocks of variables in sequence, Scotland 2001–2007 and 2010 (Scottish Household Survey).

Step	Blocks included	χ^2	Deg Frdm (no of Vars)	−2 Log Likelihood	Reduction in −2LL	Pseudo R^2 Nagelkerke	% of total Redn LL
1	One variable	36.7	1	40,878.9		0.001
2	DEM	4413.5	8	36,502.1	4376.8	0.128	37.8
3	Add POV	6460.7	11	33,735.0	2767.1	0.189	23.9
4a	Add LM (Indiv)	6832.8	18	33,362.9	3139.2	0.200	27.1
4b	Add LM (Area)	7009.4	20	33,186.3	176.6	0.205	1.5
5a	Add HSG (Indiv)	8090.7	22	32,105.0	1081.3	0.235	9.3
5b	Add HSG (Area)	8118.9	25	32,076.9	28.1	0.236	0.2
	Alternate Sequence B
3	Add HSG	7132.3	15	33,081.0	3421.1	0.208	29.6
4	Add POV	7845.6	18	32,350.2	730.8	0.228	6.3
5	Add LM	8118.9	25	32,076.9	273.3	0.236	2.4
	Alternate Sequence C
3	Add LM	5499.0	15	34,714.3	1787.8	0.162	15.5
4	Add HSG	7605.6	22	32,607.7	2106.6	0.221	18.2
5	Add POV	8118.9	25	32,076.9	530.8	0.236	4.6

Notes: All increments in chi-square are significant at 0.1% level. Nagelkerke Pseudo-R-Square statistic is a rescaling of Cox & Snell R-square (itself a generalization of R-squared in OLS regression, based on 1 minus the ratio of the Likelihoods of the null model to the fitted model) with values between 0 and 1 (Allison, 2013). The final column shows the preferred measure of contribution to the model’s explanation, the percent share of the total reduction in –2x Log Likelihood.

Table 3. Impact on probability of experiencing homelessness of selected scenarios on four illustrative cases of individuals, Scotland 2001–2007 and 2010 (Scottish Household Survey).

Scenario	A	B	C	D
	Single	Lone Parent	Parents	Single
	Working	Pt wk	Unem	Sick/Dis
	Priv rent	Soc rent	Soc rent	Soc rent
Baseline probability ever homeless	0.113	0.480	0.220	0.559
1. High unem/pov	0.162	0.545	0.268	0.622
2. High hsg mkt pressure	0.130	0.520	0.249	0.598
3. Low hsg mkt pressure, high unem/pov	0.127	0.515	0.244	0.593
4. Low hsg mkt press, high unem/pov + in work	0.437	0.630	0.244	0.593
5. High hsg mkt pressure, low unem/pov	0.156	0.573	0.290	0.648
6. High hsg mkt pressure, low unem/pov + out of work	0.156	0.573	0.092	0.358

Table 4. Logistic regression model for adults reporting having ever experienced homelessness, England & Scotland 2012 (UK Poverty and Social Exclusion Survey).

Variable description	Level	Block	Coeff B	Sig.	Exp(B)
Aged 25–34	IND	DEM	−.431	.018	.650
Aged 65 & over	IND	DEM	−.601	.002	.548
Married	IND	DEM	−.344	.016	.709
Asian hhd repres	IND	DEM	−1.221	.002	.295
Income-related benefits	HH	POV	.319	.074	1.376
Hhd with 3+ material depriv’s	HH	POV	.346	.016	1.414
More often lived in poverty	IND	POV	.379	.000	1.460
Working household	HH	LM	−.520	.054	.594
Working individual	IND	LM	.592	.027	1.808
Months unemployed	IND	LM	.009	.019	1.009
Part time emp’t rate	LA	LM	−.071	.058	.932
Social renting hhd	HH	HSG	1.042	.000	2.834
Private renting hhd	HH	HSG	.773	.000	2.167
Relative house price	TTWA	HSG	.418	.014	1.519
General health scale	IND	HLE	.241	.001	1.273
Major health problem	IND	HLE	.306	.078	1.357
Criminal record	IND	HLE	1.306	.000	3.692
Constant			−4.030	.000	.018
Model summary		−2 Log	R^2	R^2	χ^2
		Likelihood	Cox/Snell	Nagelkerke	(17 df)
		1925.9	0.140	0.304	621.9

Notes: Level – as Table 1 except HH = household; TTWA = Travel to Work Area. Block – as Table 1 except ‘HLE’ = Health and Life Events.

The following variables were tested but omitted as insignificant: aged under 25; female; lone parent, single or multi-adult household type; mixed or ‘other’ ethnicity; long-term sickness/disability; neighbourhood deprivation decile; having income below 60% of median before housing costs; no qualifications; household with 2+ workers; area ILO unemployment rate; log of population sparsity; current housing affordability problem; recently lost job; been in prison.

A cut-off of 0.16 on the predicted homelessness probability value yields a number of predicted positives close to the observed total, with correct positive predictions then representing 36% of actual homeless number.

Table 5. Comparison of performance of PSE models including blocks of variables in sequence, England & Scotland 2012 (UK Poverty and Social Exclusion Survey).

Blocks included	χ^2	Deg Frdm (no of  Vars)	−2 Log Likelihood	Reduction in −2LL	Pseudo R^2 Nagelkerke	% red’n in −2LL
One variable	1.175	1	2550.4		0.001
DEM	138.1	4	2413.5	−136.9	0.071	21.9
Add POV	468.8	7	2079.6	−333.9	0.233	53.5
Add LM	501.3	11	2047.1	−32.5	0.248	5.2
Add HSG	553.4	14	1995.0	−52.1	0.272	8.3
Add HLE	621.9	17	1925.9	−69.1	0.304	11.1
Alternate sequence
Add HLE	355.9	7	2192.7	−220.8	0.179	35.4
Add POV	543.4	10	2004.5	−188.2	0.268	30.1
Add LM	576.7	14	1971.1	−33.4	0.283	5.3
Add HM	621.9	17	1925.9	−45.2	0.304	7.2
Add HM after DEM	393.6	7	2157.9	−255.6	0.197	40.9
Add LM after DEM	297.5	8	2254.0	−159.5	0.151	25.5

Table 6. Logistic regression model for experience of homlessness between ages of 16 and 30 in British Cohort Study 1970, Great Britain 1970–2000.

Variable description	Block	Coeff B	Sig.	Exp(B)
Female	DEM	.195	.059	1.215
Mixed ethnicity		.843	.070	2.324
Other ethnicity (incl Chinese)		.820	.056	2.271
In rented housing age 10	CPOV	.298	.005	1.347
Propn consumer durables lacked age 10		.415	.052	1.514
Household income £/wk/head age 16		−.003	.047	.997
Living in rural area age 16	GEOG	−.411	.008	.663
Living in northern English regions age 16		−.326	.005	.722
Living in Scotland age 26		−.745	.004	.475
Ever in care by 16	TEXP	.630	.001	1.877
Excluded from school age 16		.884	.012	2.420
Serious drug use age 16		.896	.006	2.450
Not living with both nat parents at 16		.510	.000	1.665
Accident, hosp or nervous prob at 16		.281	.054	1.325
Mother malaise score high at 16		.336	.044	1.399
Left full-time education later	ADEC	−.079	.002	.924
Any unemployment up to age 26		.302	.013	1.353
In rented housing as sep hhd age 26		.790	.000	2.204
Living with parents age 26		−.758	.001	.469
Long term illness/disability age 26	AFLE	.345	.023	1.412
In a relationship age 26		−.870	.000	.419
Has own natural children age 26		.448	.001	1.565
Constant		−1.642	.000	.194
Model Summary	−2 Log	R^2	R^2	χ^2
	Likelihood	Cox/Snell	Nagelkerke	(22 d f)
	3222.3	0.042	0.112	324.7

Notes: Variables tested but omitted from final model include: DEM: Black, Asian ethnicity; CPOV: Free School Meals at 10; father low social class at 10; low income, renting, OR; parents with no qualifications at 16; father/mother not work or unemployed at 10; no male household head at 10; small accommodation, no car at 10; father/mother limited education; GEOG: inner urban council estate at 10; City, London, Wales, N. Ireland at 16; TEXP: truanted, convicted or cautioned at 16; malaise score at 16; ADEC: never had full time job by 26; Special Educational Need at 16; no or low qualifications at 16; left education at 26. AFLE: malaise score at 26; accident or assault by 26.

A cut-off of 0.15 on the predicted homelessness value yields a number of predicted positives close to the observed total, with correct positive predictions then representing 22% of actual homeless number.

Table 7. Comparison of Performance of British Cohort Study 1970 Models including blocks of variables in sequence, Great Britain 1970–2000.

Block	χ^2	deg frdm	−2 Log Likelihood	Increment to −2LL	Pseudo R^2 Nagelkerke	Share of total reduction 2LL
One Variable	1.97	1	3767.5		0.001
DEM	10.90	3	3758.6	−8.9	0.004	1.6%
CPOV	69.30	6	3477.7	−280.9	0.024	51.5%
GEOG	101.40	9	3445.6	−32.1	0.036	5.9%
TEXP	180.30	15	3366.7	−78.9	0.063	14.5%
ADEC	267.50	19	3279.6	−87.1	0.093	16.0%
AFLE	324.70	22	3222.3	−57.3	0.112	10.5%

Allison, P. (2013) What’s the best R-Squared for logistic regression. Available at http://statisticalhorizons.com/r2logistic (accessed 13 February 2013).

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