Reporting uses *random iterative method* (RIM) weighting within reports. This is an iterative approach in which the algorithm tries to weight responses. The algorithm runs various iterations based on the inputs it receives in the setup of the weight scheme until it achieves convergence based on the provided parameters. *Convergence* occurs when the algorithm succeeds in finding a weight scheme across responses that meets the targets applied to each criteria.

As an example, let's look at how a multivariable weight scheme can be achieved between age and gender. Based on the responses received for this survey and the way age and gender are categorized, we have the following spread of responses:

A user then defines the weight scheme by providing a target percentage relative to the initial sample percentage:

When we overlay these inputs onto the original response data (and convert counts to percentages), we get the following result:

We can see the initial sample percentages as well as the targets we want the algorithm to try and converge to. Next, the algorithm applies weights to the initial response data and tries to meet the target percentage for both inputs.

The algorithm runs various iterations where it modifies weights applied to the row and column values until it reaches convergence and produces the final weighting assignments. With multivariable weighting, the outcome from one scenario is used as an input in the next weighting variable (i.e. we have a third variable in our weighting scheme). This process is repeated until convergence is reached and a corresponding weight is assigned to each response.

In the above example, the weights assigned to each response are:

Individual weights applied to a response are available in report exports so you can see how the algorithm weighted each response based on both variables (the age and gender of a respondent).

At the moment, a user cannot provide our weighting calculation with any input beyond the target percentages and the variables to use in the weight scheme. Other tools may allow greater control such as applying weight trimming (defining the maximum or minimum weights that can be used). However, this can decrease the chances of the algorithm reaching convergence. Alida's preference is for the algorithm to achieve the weight scheme defined by the user and inform the user of what it did to make this possible.

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