Double ratio estimation within a design-based nonresponse bias mitigation strategy

Abstract In the national forest inventory of the USA, there is an ongoing issue with sample plots that are either completely or partially unmeasured due to access issues such as hazardous conditions or lack of permission. The nonrandom nature of the nonresponse in the general population potentially creates a bias in the sample and resulting estimations. A potential mitigation option is the use of response homogeneity groups in combination with ratio-to-size estimators. This paper presents an extension of this approach where per-unit area estimates commonly useful to practitioners, e.g. number of trees per hectare, take the form of a double ratio (a ratio of ratios). Further complexity arises in the case of nested plot designs where attributes of interest need to be combined across plot sizes whose nonresponse rates may differ. The estimation details and associated formulae are presented and subsequently assessed using Monte Carlo simulation. The response homogeneity group ratio estimates appeared to be unbiased, but the approximate variances were substantially overestimated due to an overly large estimated covariance term. An alternative formulation of the estimated covariance produced overall variance estimates that aligned better with the simulation results but still were overestimated by ~10% to 15%. The standard estimation approach resulted in the estimate being too large (0.3%) with an overall variance that was too small (−6.3%) due to substantially underestimated component variance and covariance terms. Thus, response homogeneity group estimation methods can produce unbiased per-unit area estimates in the presence of nonresponse, although it appears the estimated variance is somewhat conservative.