Detroit Metro Area Communities Study (DMACS) Wave 3, Michigan, 2018

Statistical weighting to control for the impacts of the sample design and non-response was performed in three stages: Design weight: A design weight of 1 was assigned to existing panel members, who were drawn from a simple random sample of the City. For newly-sampled households, respondents were assigned a design weight that was equal to the inverse of the selection probability (the number of households in the city as estimated by the Census, divided by the number of sampled households in the block group). This was then divided by a constant to adjust the scale of the weights to a mean of 1. Non-response weight: Non-response weights were calculated separately for the returning panelists and the new Wave 3 sample members. For the returning panelists, steps in generating this weight included:Factor analysis on 13 block-group variables from the 2011-2015 American Community Survey to reduce the number of potential predictors;Multiple imputation by chained equations to impute 25 datasets with complete W1 data for all respondents;Examination of the bivariate relationships between Wave 3 response and potential predictors, including ACS data, Wave 1 responses, and paradata from Waves 1 and 3;Running a response propensity model on all 25 imputed datsets. This model was an unweighted logit model using limited set of predictors (those where p <.1 in the bivariate relationship to W3 response).Smoothing the weights generated by creating quintile groupings of the inverse of the predicted probability of responseFor the new Wave 3 sample members, the process was very similar; though the potential predictors available were fewer, and without prior data, the multiple imputation phase was not necessary. In addition,Factor analysis was conducted on 15 block-group variables from the 2012-2016 American Community Survey rather than the 13 from the earlier wave of the ACS that were attached to Wave 1;The selected response propensity model was a weighted logit model that included ACS factor scores as predictors and random effects for block group. This model was selected as the preferred model because (a) it includes the design weights for selecting the new wave 3 sample, (b) the random effects for block groups (our primary sampling units) were significant, and (c) it produced the least amount of variance in predicted probabilities of the potential models tested.Post-stratification weight: after multiplying the design weight by the non-response weight, an additional post-stratification weight was developed to calibrate the demographic distribution of respondents to the target population of the City of Detroit. We first used multiple imputation to create ten datasets that were complete for all respondents for the variables used in raking. In order to preserve the correlations between these variables and other survey outcomes, a larger set of variables was imputed, including income, length of residence at current address and length of residence in Detroit, number of places R has lived in last five years, home ownership, whether R ever experienced homelessness, marital status, internet access at home, neighborhood satisfaction, views on community assets (Q6a-k), views on priorities to improve public health (Q7a-q), fear of crime, support from social networks, whether Rs neighborhood has name, primary source of health care, insurance status, affiliation with community associations, ability to pay for current care or health emergency, attendance of religious services, and political ideology. The predictors for these imputation models included ACS factor scores (see step 3a) and other wave 3 variables for which there were no missing data. This weight was developed with an iterative proportional fitting (raking) procedure (using the "ipfraking" package in Stata 15) and includes adjustments for age, gender, race, Hispanic ethnicity, and education to match the American Community Survey (ACS) 2012-2016 estimates for the population 18 and older in the City of Detroit. Weights were trimmed to a maximum value of 4.

本研究采用三阶段统计加权方法，以控制抽样设计与无应答偏倚带来的影响：
1. **设计权重**：针对从底特律市简单随机抽样抽取的固定追踪面板成员，为其赋予设计权重1。对于新抽选的家庭，受访者的设计权重等于抽选概率的倒数（即人口普查估算的全市家庭总数除以街区组内抽选家庭数）；随后将该权重除以一个常数，使权重均值调整为1。
2. **无应答权重**：分别为续访追踪面板成员与新加入第三波（Wave 3）的样本成员计算无应答权重。
- 针对续访追踪面板成员，该权重的生成步骤包括：
1. 基于2011-2015年美国社区调查（American Community Survey, ACS）的13项街区组变量开展因子分析，以缩减潜在预测变量的数量；
2. 采用链式方程多重插补（Multiple imputation by chained equations）生成25份包含所有受访者完整第一波（Wave 1）调查数据的完整数据集；
3. 考察第三波调查应答情况与潜在预测变量间的双变量关联，潜在预测变量涵盖ACS数据、第一波调查应答结果以及第一、三波调查的过程辅助数据；
4. 基于全部25份插补数据集构建响应倾向模型：该模型为未加权logit模型，仅纳入与第三波应答存在p<0.1双变量关联的有限预测变量集；
5. 通过对预测应答概率的倒数进行五分位分组，对生成的权重进行平滑处理。
- 针对新加入第三波的样本成员，其无应答权重的生成流程大体相似，但由于可用潜在预测变量更少且无前期调查数据，因此无需开展多重插补步骤。此外，本次分析采用2012-2016年美国社区调查的15项街区组变量，而非与第一波调查绑定的早期ACS调查的13项变量；最终选用的响应倾向模型为加权logit模型，以ACS因子得分作为预测变量，并纳入街区组（本研究的主要抽样单元）的随机效应。选择该模型作为最优模型的依据包括：(a) 其纳入了第三波新样本的抽选设计权重；(b) 街区组的随机效应具有统计学显著性；(c) 在所有测试的候选模型中，该模型生成的预测应答概率的方差最小。
3. **后分层权重**：在将设计权重与无应答权重相乘后，本研究进一步构建后分层权重，以校准受访者的人口统计学分布，使其匹配底特律市的目标总体。首先，采用链式方程多重插补生成10份包含所有受访者完整调查数据的数据集，用于后续的迭代比例拟合（raking）分析；为保留这些变量与其他调查结果间的相关性，本次插补纳入了更广泛的变量集，包括受访者的收入、当前住址居住时长、在底特律的居住时长、过去五年内的居住地点数量、房屋所有权、是否曾无家可归、婚姻状况、家庭互联网接入情况、社区满意度、对社区资产的看法（问题Q6a-k）、对改善公共卫生优先级的看法（问题Q7a-q）、犯罪恐惧程度、社会网络支持情况、所在街区是否有专属名称、主要医疗保健来源、保险参保状态、社区协会参与情况、支付当前医疗费用或突发医疗费用的能力、宗教礼拜出席情况以及政治意识形态。上述插补模型的预测变量包括ACS因子得分以及第三波调查中无缺失值的其他变量。本权重通过迭代比例拟合（raking）程序构建（使用Stata 15中的`ipfraking`包），并针对年龄、性别、种族、西班牙裔族裔与教育程度进行调整，使其匹配2012-2016年美国社区调查中底特律市18岁及以上人口的估算值。最终将权重截断至最大值4。