Table 2.
Multi-collinearity analysis
| Variable # | Variable name | Transformationa | Tolerance | VIF | Decision |
|---|---|---|---|---|---|
| 2 | Adult social-care users who have as much social contact as they would like | – | 0.64 | 1.57 | Keep |
| 3 | Adults in treatment at specialist alcohol misuse services | Log | 0.31 | 3.24 | Keep |
| 4 | Adults in treatment at specialist drug misuse services | Log | 0.08 | 12.66 | Remove |
| 5 | Alcohol-related hospital admission (female) | Log | 0.00 | 422.64 | Remove |
| 6 | Alcohol-related hospital admission (male) | Log | 0.00 | 1126.14 | Remove |
| 7 | Alcohol-related hospital admission (all) | Log | 0.00 | 2813.20 | Keep |
| 8 | Children in the youth justice system | Log | 0.36 | 2.74 | Keep |
| 9 | Children leaving care | Log | 0.22 | 4.56 | Keep |
| 10 | Depression recorded prevalence | – | 0.39 | 2.59 | Keep |
| 11 | Domestic abuse incidents | – | 0.49 | 2.03 | Keep |
| 12 | Emergency hospital admissions for intentional self-harm (female) | square root | 0.08 | 13.18 | Remove |
| 13 | Emergency hospital admissions for intentional self-harm (male) | square root | 0.06 | 17.53 | Remove |
| 14 | Emergency hospital admissions for intentional self-harm (all) | square root | 0.00 | 11956.59 | Keep |
| 15 | Looked after children | Log | 0.19 | 5.35 | Remove |
| 16 | Self-reported well-being - high anxiety | – | 0.65 | 1.53 | Keep |
| 17 | Severe mental illness recorded prevalence | Log | 0.30 | 3.30 | Keep |
| 18 | Social care mental health clients receiving services | Log | 0.75 | 1.34 | Keep |
| 19 | Statutory homelessness | Log | 0.41 | 2.41 | Keep |
| 20 | Successful completion of alcohol treatment | – | 0.45 | 2.22 | Keep |
| 21 | Successful completion of drug treatment - non-opiate users | – | 0.41 | 2.47 | Keep |
| 22 | Successful completion of drug treatment - opiate users | Log | 0.49 | 2.02 | Keep |
| 23 | Unemployment | Log | 0.16 | 6.40 | Keep |
| 24 | Adult carers who have as much social contact as they would like (18+ yrs) | – | 0.00 | infinity | Remove |
| 25 | Adult carers who have as much social contact as they would like (all ages) | – | 0.59 | 1.71 | Keep |
| 26 | Estimated prevalence of opiates and/or crack cocaine use | Log | 0.09 | 10.60 | Keep |
| 27 | Long-term health problems or disability | – | 0.08 | 12.84 | Remove |
| 28 | Marital breakup | – | 0.39 | 2.59 | Keep |
| 29 | Older people living alone | – | 0.08 | 11.77 | Remove |
| 30 | People living alone | Inverse | 0.23 | 4.36 | Keep |
| 31 | Self-reported well-being - low happiness | – | 0.36 | 2.77 | Keep |
aSee Additional file 1