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.

本研究针对抽样设计与无应答带来的影响，通过三阶段流程完成统计加权校准：

### 设计权重
针对从该市简单随机抽样中抽取的现有追踪面板成员，为其赋予设计权重1。对于新抽中的家庭户，为受访者分配的设计权重等于抽样概率的倒数（即普查估算的全市家庭户总数除以该街区组内抽中家庭户的数量）。随后将该权重除以一个常数，以将权重尺度调整至均值为1。

### 无应答权重
无应答权重需分别为追踪回访成员与新纳入的第三波（Wave 3）抽样成员计算。

#### 针对回访的追踪面板成员
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个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）调查数据的数据集；
3. 考察第三波应答情况与潜在预测变量间的双变量关联，预测变量涵盖ACS数据、第一波调查应答结果以及第一、三波的调查辅助数据；
4. 在全部25份插补数据集上运行应答倾向模型：该模型为未加权logit模型，仅选用在与第三波应答的双变量关联中p<0.1的有限预测变量子集；
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。

#### 针对新纳入的第三波抽样成员
流程大体与回访成员一致，但可用的潜在预测变量更少，且无前期调查数据，因此无需执行多重插补步骤。此外存在两处差异：
1. 因子分析基于2012-2016年美国社区调查（ACS）的15个街区组变量开展，而非匹配第一波调查所用的2011-2015年ACS的13个变量；
2. 最终选用的应答倾向模型为加权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样设计权重；(b) 作为主要抽样单元的街区组随机效应显著；(c) 在所测试的所有候选模型中，该模型生成的预测应答概率方差最小。

### 后分层权重
在将设计权重与无应答权重相乘后，需进一步构建后分层权重，以将受访者的人口统计学分布校准至底特律市的目标总体。具体流程如下：
1. 采用多重插补生成10份完整数据集，涵盖所有受访者用于raking加权的全部变量；
2. 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，包括收入、当前住址居住时长、在底特律的居住时长、过去5年居住过的地点数量、房屋所有权、受访者是否曾无家可归、婚姻状况、家庭互联网接入情况、社区满意度、社区资产认知（问题Q6a-k）、改善公共卫生的优先级认知（问题Q7a-q）、犯罪恐惧感、社会网络支持情况、受访者所在社区是否有正式名称、主要医疗保健来源、保险状态、社区协会成员身份、支付当前医疗费用或突发医疗费用的能力、宗教仪式出席情况以及政治意识形态；
3. 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；
4. 该权重通过迭代比例拟合（raking）程序构建，使用Stata 15中的`ipfraking`包，针对年龄、性别、种族、西班牙裔族裔与教育程度进行调整，以匹配2012-2016年ACS中底特律市18岁及以上人口的估计值；
5. 最终将权重截断至最大值为4。