Variance Estimation. To obtain estimates of variability (such as the standard error of sample estimates or corresponding confidence intervals) for estimates based on MEPS survey data, one needs to take into account the complex sample design of MEPS. Various approaches can be used to develop such estimates of variance including use of the Xxxxxx series or various replication methodologies. Replicate weights have not been developed for the MEPS 1998 data. Variables needed to implement a Xxxxxx series estimation approach are provided in the file and are described in the paragraph below. Using a Xxxxxx Series approach, variance estimation strata and the variance estimation PSUs within these strata must be specified. The corresponding variables on the MEPS full year utilization database are VARSTR98 and VARPSU98, respectively. Specifying a “with replacement” design in a computer software package such as SUDAAN (Xxxx et al, 1996) should provide standard errors appropriate for assessing the variability of MEPS survey estimates. It should be noted that the number of degrees of freedom associated with estimates of variability indicated by such a package may not appropriately reflect the actual number available. For MEPS sample estimates for characteristics generally distributed throughout the country (and thus the sample PSUs), there are over 100 degrees of freedom associated with the corresponding estimates of variance. The following illustrates these concepts using two examples from Section 4.2. Using a Xxxxxx Series approach, specifying VARSTR98 and VARPSU98 as the variance estimation strata and PSUs (within these strata) respectively and specifying a with replacement design in a computer software package SUDAAN will yield standard error estimates of $2.93 and 0.0080 for the estimated mean of out-of-pocket payment and the estimated mean proportion of total expenditures paid by private insurance respectively.
Variance Estimation. (XXXXXX, VARSTR)
Variance Estimation. (VARSTR00, VARPSU00) Examples 2 and 3 from Section 4.2
Variance Estimation. To obtain estimates of variability (such as the standard error of sample estimates or corresponding confidence intervals) for estimates based on MEPS survey data, the complex sample design of MEPS for both person and family level analyses must be taken into account. Various approaches can be used to develop such estimates of variance including use of the Xxxxxx series or replication methodologies. Replicate weights have not been developed for the MEPS 1997 data. Using a Xxxxxx Series approach, variance estimation strata and the variance estimation PSUs within these strata must be specified. The corresponding variables on the 1997 MEPS full year utilization database are VARSTR97 and VARPSU97, respectively. Specifying a “with replacement” design in a computer software package, such as SUDAAN, should provide standard errors appropriate for assessing the variability of MEPS survey estimates. It should be noted that the number of degrees of freedom associated with estimates of variability indicated by such a package may not appropriately reflect the actual number available. For MEPS sample estimates for characteristics generally distributed throughout the country (and thus the sample PSUs), there are over 100 degrees of freedom for the 1997 full year data associated with the corresponding estimates of variance.
Variance Estimation. (XXXXXX, VARSTR)
1. When pooling any year from 2002 or later, one can use the variance strata numbering as is.
2. When pooling any year from 1996 to 2001 with any year from 2002 or later, use the H36 file.
3. A new H36 file will be constructed in the future to allow pooling of 2007 and later years with 1996 to 2006.
Variance Estimation. Variance provides a means of assessing and reporting the precision of a point estimate, playing a critical role in the interval estimation, hypothesis testing, and power calculation. In this section, asymptotic variance formulas for different IRA statistics in the review are summarized, which allows approximate variance estimations for those IRA measures based Xxxxxx-corrected IRA statistics with ICC interpretations Xxxxxxx and Xxxxxxxx’s 𝑟11 Equal when 𝑛10 = 𝑛01 Mak’s 𝜌˜ Xxxxx’x κ Equal when 𝑛10 = 𝑛01 Xxxxx’x π Equal when 𝑛11= 𝑛00 Equal when 𝑛11 = 𝑛00 and 𝑛10 = 𝑛01 Xxxxxxxxxxxx’s α Xxx Xxxx’x 𝐼2 r Gwet’s 𝐴𝐶1 on the observed data from Table 1. e|κ Xxxxxx, Xxxxx, and Xxxxxxx [47] proposed a variance estimator for Xxxxx’x κ under the nonnull case of IRA, and Gwet [12] rewrote the variance formula under the two-rater case for better comparability with the estimated variances of several other IRA statistics. The estimated variance of κ is given as Vˆar(κ) = npˆ (1 − pˆ ) − 4(1 − κ) pˆ ωˆ + pˆ (1 − ωˆ) − κpˆ N (1 − pˆe|κ )2 11 00 + 4(1 − κ)2 pˆ ωˆ2 + 1 pˆ (2pˆ + pˆ )2 + 1 pˆ 01 01 10 00 (2pˆ + pˆ )2 + pˆ (1 − ωˆ)2 ,, where ωˆ = pˆ11 + pˆ10/2 + pˆ01/2. The performance of this large-sample variance of κ have been evaluated via Monte Carlo simulations in Xxxxxxxxx and Xxxxxx [48] and Fleiss and Xxxxxxxxx [49]. ˆ For Xxxxxxx et al.’s S and the several equivalent IRA measures mentioned in the review, since the asymptotic variance estimator of percent agreement could be obtained as Var(pˆa) = pˆa(1 − pˆa)/N based on the binomial properties, we can get the variance estimator for S = 2pˆa − 1 as ˆ Var(S) = N pˆa(1 − pˆa). For Xxxxx’x π, Gwet [12] proposed a nonparametric variance estimator with linearization techniques to remedy the formula proposed by Xxxxxx [50], which was under the hypothesis of no agreement and was not valid for building up confidence intervals. Under our scenario of interest, the variance formula of π can be written as 1 N (1 − pˆe|π )2 11 Vˆar(π) = npˆ (1 − pˆ ) − 4(1 − π) pˆ 00 e|π ωˆ + pˆ (1 − ωˆ) − pˆ pˆ 11 ˆ + ( 4 10 01 00 + 4(1 − π)2 pˆ ω2 pˆ + pˆ ) + pˆ
(1 − ωˆ)2 − pˆ2 ,. e|π Regarding Gwet’s AC1, Gwet [12] utilized a linear approximation that included all terms with a stochastic order of magnitude up to N−1/2 to derive a consistent variance estimator. The variance formula of AC1 is given by Vˆar(AC ) = npˆ (1 − pˆ ) − 4(1 − AC ) pˆ (1 − ωˆ) + pˆ ωˆ − pˆ pˆ N (1 − pˆe|AC1 )2 1 11 1 11 ˆ) + ( 4 + 4(1 − AC )2 pˆ
Variance Estimation. The MEPS is based on a complex sample design. To obtain estimates of variability (such as the standard error of sample estimates or corresponding confidence intervals) for MEPS estimates, analysts need to take into account the complex sample design of MEPS for both person-level and family-level analyses. Several methodologies have been developed for estimating standard errors for surveys with a complex sample design, including the Xxxxxx-series linearization method, balanced repeated replication, and jackknife replication. Various software packages provide analysts with the capability of implementing these methodologies. MEPS analysts most commonly use the Xxxxxx Series approach. However, an option is also provided to apply the BRR approach when needed to develop variances for more complex estimators.
