## Modeling Superpopulation Variance: Its Relationship to Total Survey Error

### by James R. Knaub, Jr.

**Abstract:**
In repeated surveys there generally are auxiliary/regressor data available for all members of the population, that are related to data collected in a current sample or census survey. With regard to modeling, these regressor data can be used to edit the current data through scatterplots, and to impute for missing data through regression. Another use for regressor data may be the study of total survey error. To do this, follow these steps: (1) stratify data by regression model application (the related scatterplots can be used for editing); (2) find predicted values for data not collected, if any, and (3) replace all data that are collected with corresponding predicted values. If model-based ratio prediction is used, variance proportionate to a measure of 'size,' then the sum of the predicted values equals the sum of the observed values they replace. (See "Fun Facts" near the end of this article: fact # 4.) The standard error of the total of the predicted values for every member of a finite population, divided by that total, and expressed as a percent, could be labeled as an estimated relative standard error under a superpopulation, or a model-based RSESP. This RSESP would be influenced by (1) the models chosen, (2) inherent variance, and (3) total survey error (sampling and nonsampling error). This article proposes this model-based RSESP as a survey performance indicator and provides background and examples using both real and artificial data.
**Key Words: **
regression model; performance measure; scatterplot edits; inherent variance; nonsampling error; sampling error; total survey error

**Author:**

James R. Knaub, Jr., james.knaub@eia.doe.gov

**Editor:**
Simos G. Meintanis,simosmei@econ.uoa.gr

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