BMC Public Health 2007, 7:285 http://www.biomedcentral.com/1471-2458/7/285 sion scale [35]: "I visit my friends in their homes", "The friendships and associations I have with other people in my neighbourhood mean a lot to me", "If I need advice about something I could go to someone in my neighbour- hood", "I believe my neighbours would help in an emer- gency", "I borrow things and exchange favours with my neighbours", "I would be willing to work together with others on something to improve my neighbourhood", "I rarely have a neighbour over to my house to visit", and "I regularly stop and talk with people in my neighbour- hood". A five-point response scale was used, with the fol- lowing categories 1: "strongly agree", 2: "agree", 3: "neither agree nor disagree", 4: "disagree", and 5: "strongly disagree". Responses to the eight statements were summed, forming an internally consistent scale (Cronbach's α = 0.81) [19,36]. The individual neighbourhood perception scales were transformed into four contextual variables at the neigh- bourhood (ED) level. As the neighbourhood perception scales may have a multilevel structure of their own [37], we conducted separate two-level random-coefficient regression analyses for each of the four neighbourhood perception scales. The four individual neighbourhood perception scales were fitted in turn as dependent varia- bles, and were assumed to have a normal distribution. The models were 'null' with no independent variables. The analyses showed that 23.2%, 15.0%, 16.2%, and 1.8% of the variation could be found at the neighbourhood level for access to amenities, neighbourhood quality, neigh- bourhood disorder and social cohesion respectively. This suggests that there is more inter-rater agreement about the first three neighbourhood characteristics than there is about neighbourhood social cohesion. We included the standardised values (Z-scores) of the level 2 residuals in the subsequent analyses as neighbourhood-level varia- bles. The level 2 residuals of the four neighbourhood per- ception variables reflect the neighbourhood-specific contributions to the overall scores [38]. The shrunken residuals derived from multilevel modelling provide more precise estimates of neighbourhood characteristics than aggregated individual variables, as it is based on the part of the variation that may be attributed to the true varia- tion between neighbourhoods [39]. In this study we use the proportion of households with an annual gross income of under £10,000 as an indicator of neighbourhood deprivation. The cut-off point was chosen to represent the line of poverty [40]. In the absence of rou- tinely available income data at ED level, we used validated gross household income estimates from a commercial dataset (CACI Ltd's Paycheck Household Income Model) [41,42]. The Paycheck model of neighbourhood income was found to be highly correlated with the widely-used Townsend index of social and material deprivation across the 325 census EDs of Caerphilly borough (r = 0.80). The percentage of households in the 325 Caerphilly EDs with an income under £10,000 ranged from 3.8 to 73.7 (Mean = 31.3; SD = 13.0). The high percentage of low income households in some EDs reflect the high levels of socio- economic deprivation in the borough; two census wards situated in the Upper Rhymney Valley in the north of the borough are among the 5% highest ranking wards in Eng- land and Wales on both the Breadline Britain and the Work Poverty Indices [43]. The neighbourhood depriva- tion variable was standardised by calculating the Z-scores. Analysis Multilevel modelling was utilised to analyse the CHSNS dataset, with individuals as level 1 and EDs as level 2 units. A series of two-level logistic regression models were constructed with self rated health as the dependent varia- ble. The parameters were estimated using Markov Chain Monte Carlo (MCMC) procedures in MLwiN software [44]. First, we estimated the coefficients of the different individual socio-demographic variables in a single model (Model 1). Second, we estimated the coefficients of the different neighbourhood variables in three series of mod- els (Models 2a-c). In Model 2a we estimated the unad- justed associations of the five neighbourhood variables with self-rated health in separate models. In Model 2b we estimated the adjusted coefficients of the neighbourhood variables in five separate models, controlling for the indi- vidual socio-demographic variables. In Model 2c we again estimated the adjusted coefficients of the neighbourhood variables in four separate models, but now additionally controlling for neighbourhood deprivation. We further examined whether there are gender differences in the associations between the neighbourhood environ- ment and self rated health, by estimating the socio-demo- graphic-adjusted coefficients for men and women separately. Possible interactions were later validated by remodelling the complete dataset with the relevant gender interaction terms. That is, the gender interactions were tested in the combined dataset, and adjusted for differ- ences in age, social class, employment status, and home ownership. In this study several respondents had missing values on one or more of the social class, employment status and housing tenure variables (see Table 1). We dealt with these missing data through multiple imputation [45]. In multiple imputation, missing values are replaced with plausible values a number of times, to reflect the uncer- tainty about the true values of the missing data. In this study we imputed missing values based on the distribu- tion of the values for the three variables in twelve age-sex strata (using the age groups of 18–24, 25–34, 35–44, 45– 54, 55–64, and 65–74 for men and women separately). Page 4 of 10 (page number not for citation purposes)