Sample Adjustment: Principles and Methods

The iterative RAS method: gradually adjusting the sample sample A subset of the population studied, selected in accordance with a sampling plan, and subject to the collection of information. Find out more weights

The most intuitive method is RAS (Raking Adjustment Adjustment A statistical processing that aims to correct structural discrepancies on one or more variables between the sample and the entire population studied (based on a known structure, such as a census or a framing study). This processing involves the calculation of a so-called adjustment coefficient for each individual surveyed. The coefficient is then combined with the extrapolation to arrive at its weight and thus align the weighted sample's structure to the structure of the population. Find out more System or iterative proportional fitting). The principle is simple:

1. First, adjust the weights so that the margin for the first criterion criterion A computer or statistical object that groups the same information for all individuals in the study population. For example, the AGE variable represents the age of all the individuals of the population studied. Variables can be qualitative (e.g., GENDER or SPG) or quantitative (e.g., AGE or HEIGHT). Find out more (e.g., gender) is exact.

2. Then we readjust so that the margin for the second Criterion (age) is met—which may slightly distort the first margin.

3. We repeat the process for the first criterion, and so on, in a loop.

At each iteration, the weights are multiplied by the ratio of the theoretical margin to the estimated margin in the weighted sample:

The algorithm generally converges within a few iterations. Its underlying distance function is G(x) = x log log A file containing a history of events. By extension, it also describes an event in itself, for example the launch of an app on a smartphone with the launch time and the app name. Find out more (x) − x + 1, which guarantees strictly positive weights. However, it can produce very high weights if the deviations between the sample sample A subset of the population studied, selected in accordance with a sampling plan, and subject to the collection of information. Find out more and the Population Population The universe of a survey composed of basic statistical units. These units may be physical persons, households, companies, municipalities, etc. The population serves as a sampling frame for selecting a sample, and as a basis for calculation of the extrapolations from the sample. Find out more are large.

INSEE INSEE The Institut National de la Statistique et des Études Économiques (National Institute for Statistics and Economic Studies) is a general directorate of France's Ministry of the Economy, Finance, and Industry. INSEE carries out several sample surveys in the socio-economic field (households, companies), in addition to its responsibilities for the national accounts and taking the census (last completed in March 1999). This government agency is responsible for coordinating official statistics, reference data produced by the entire public statistics system. Find out more ’s CALMAR macro, a benchmark method for margin-based calibration

Developed by INSEE, the CALMAR macro (CALage sur MARges) formalizes calibration as an Optimisation Optimisation Processing by which a solution that meets pre-defined constraints is sought among a variety of possible solutions to a problem. Example: optimisation of a programme schedule under the constraint of a minimum cumulative audience, or optimisation of an advertising campaign with a budget constraint. Find out more problem: finding the weights w_k that minimize a distance function G with respect to the Survey Survey A statistical method that aims to produce information about a population by interviewing part of the population (sample). This word is generally used to mean a survey conducted on a sample that have been interviewed using a questionnaire or else systematically observed. Find out more weights d_k, subject to the calibration constraints:

The system is solved using Newton's algorithm. The CALMAR macro offers five asymptotically equivalent distance functions: in practice, the choice among them is guided by the shape of the weight weight 1. The proportion of a category of individuals in relation to the entire population. For example, on January 1st, 2020, the weight of women was 51.7% of the household population. 2. The survey weight refers to the coefficient assigned to each individual in the sample, and which corresponds to the inverse of the probability that they belong to the sample. For example, for a sample of 20,000 individuals drawn at random from a population of 40 million, the survey weight is 2,000. 3. The adjustment weight refers to the coefficient assigned to each individual after the sample adjustment, and which corresponds to the number of people in the population that are represented by this individual in the sample. Find out more distribution distribution This refers to the distribution of a variable; “structure” is also used with this meaning. In statistics, for each x value of a quantitative variable, the distribution function gives the proportion of individuals having a variable value that is less than or equal to x. Find out more and by the desire to avoid extreme values.

The Ridge approach: a more flexible method when there are many criteria

When there are many criteria or they are partially collinear, the system of equations may become unstable or fail to converge. The Ridge approach (or L2 regularization) offers a solution by adding a penalty term to the system matrix. 
In the context of parameter estimation, instead of solving β^ = (X' X)^-1 X' Y, we solve:
β^_ridge = (X' X + λI)^-1 X' Y
The parameter λ > 0 regularizes the matrix X' X by making it better conditioned: values close to zero are “raised,” which stabilizes the inversion. The trade-off is a slight bias bias The bias of a statistical result is the difference between the result obtained and the exact value that one is seeking. There are three distinct types of bias: sampling bias (for example: using an unsuitable sampling frame), observational bias (for example: poor wording of a question or answer grid), and estimate bias (for example: not fully taking into account the categories for drawing the sample). Find out more in the coefficients, offset by a substantial reduction in Variance Variance The variance of a statistical distribution is the average of the squares of the differences between the values of the distribution and their average. A standard deviation is always determined by first finding the variance, then taking the square root. Find out more .
In practice, this approach is useful when:
The number of calibration criteria is high relative to the Sample Size Sample Size The number of statistical units constituting a sample. The accuracy of a survey depends greatly on the sample size. Find out more ;
The auxiliary information is itself derived from surveys and subject to Margins of Error Error There are different types of errors in surveys : coverage error (the sampling base does not correspond exactly to the population studied), non-response error (a part of the sample does not wish to answer certain questions), measurement error (the value declared by the individual is incorrect) and sampling error (only a part of the population is observed). The combination of these errors - the total error - is the difference between the survey-estimated value and the (generally unknown) “true value” of the parameter in the population. Find out more ;
A “flexible” calibration is desired that does not strictly adhere to the margins but produces more stable weights.