BMC Public Health 2004, 4 http://www.biomedcentral.com/1471-2458/4/22 Table 1: Items in the short form Household Food Security Scale [4]. Figures are frequencies (column percent) except where stated. Number Designation Question Affirmative responses (531) Item-score correlation Estimated Thresholda (SE) Item fit P value 3 2 5 8 7 10 'Balanced meal' I/we couldn't afford to eat balanced meals Affirmative: Often or sometimes true 'Food last' The food that I/we bought just didn't last, and I/we didn't have money to get more Affirmative: Often or sometimes true 'Skip meals' In the last 12 months, since (date 12 months ago) did you (or other adults in your household) ever cut the size of your meals or skip meals because there wasn't enough money for food? 'How often' If YES, How often did this happen? Affirmative: Almost every month or Some months but not every month 'Eat less' In the last 12 months, did you ever eat less than you felt you should because there wasn't enough money to buy food? 'Hungry' In the last 12 months, since (date 12 months ago) were you ever hungry but didn't eat because you couldn't afford enough food? Cronbach's alpha 162 (31) 109 (21) 93 (18) 70 (13) 75 (14) 31 (6) 0.56 0.73 0.76 0.61 0.79 0.52 0.87b -2.027 (0.063) -0.749 (0.072) -0.252 (0.095) 0.476 (0.099) 0.300 (0.108) 2.251 (0.116) <0.001 <0.001 0.026 <0.001 <0.001 <0.001 a under Rasch model convention thresholds are scaled so arithmetic mean is zero b Cronbach's alpha for six item scale sample has been included in previous reports [7]. The study received research ethics committee approval and subjects gave informed consent to participation. Analysis Each item in the household food security scale was reduced to the categories of affirmative or not as described by Blumberg et al [4] (Table 1). We estimated Cronbach's alpha for the six items. We estimated the intraclass corre- lation coefficient for each item using analysis of variance in order to assess the correlation of item responses within households. Item response models were fitted to the data using BILOG-MG version 3.0 software from Scientific Software International [17]. Item-score correlations were estimated as the Pearson correlation between each item and the total and were taken from the BILOG output [17]. Initially a one parameter logistic (Rasch) model was fit- ted. Item thresholds, their standard errors and item fit P- values are reported. Item thresholds are estimated param- eters which indicate the location of the item in relation to the latent construct. In this context, the threshold pro- vides a measure of the relative severity of food insecurity associated with affirmative responses to an item. Under the conventions of the Rasch model, the item thresholds are scaled so that their arithmetic mean is zero. The thresholds may also be rescaled to a different mean loca- tion as discussed by Bickel et al [5]. After fitting the single group model, we explored whether there was evidence of differential item functioning in dif- ferent ethnic groups. Subjects with 'not known' ethnic group were omitted from these analyses. The combined data from the three ethnic groups were fitted to a one- parameter logistic model, but with separate item thresh- olds estimated for each ethnic group. Only the means of the item thresholds were constrained to be equal across groups. The extent to which items functioned differen- tially in the three ethnic groups was then assessed by the likelihood ratio (difference in twice log likelihood) between the single-group model with item thresholds constrained to be equal for all respondents and this unconstrained model. We used logistic regression to estimate associations between item responses, as dependent variables, and income. The slope index of inequality for income was esti- mated as recommended by Mackenbach and Kunst [18] and Wagstaff et al [19]. This permitted the use of a single estimate to summarise the association between income and an item, rather than requiring the presentation of odds ratios for each category of income. Logistic regres- Page 3 of 9 (page number not for citation purposes)