Quasi-variance (qv)
estimates
In the Westminster system of government, the ''Estimates'' are an outline of government spending for the following fiscal year presented by the Cabinet (government), cabinet to parliament. The Estimates are drawn up by bureaucrats in the finance ...
are a statistical approach that is suitable for communicating the effects of a
categorical explanatory variable within a
statistical model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of Sample (statistics), sample data (and similar data from a larger Statistical population, population). A statistical model repre ...
. In standard statistical models the effects of a categorical explanatory variable are assessed by comparing one category (or level) that is set as a benchmark against which all other categories are compared. The benchmark category is usually referred to as the 'reference' or 'base' category. In order for comparisons to be made the reference category is arbitrarily fixed to zero. Statistical data analysis software usually undertakes formal comparisons of whether or not each level of the categorical variable differs from the reference category. These comparisons generate the well known ‘significance values’ of parameter estimates (i.e., coefficients). Whilst it is straightforward to compare any one category with the reference category, it is more difficult to formally compare two other categories (or levels) of an explanatory variable with each other when neither is the reference category. This is known as the reference category problem.
Quasi-variances are approximations of
variance
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion ...
s. Quasi-variances are statistics associated with the
parameter estimate
A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
s (coefficients) of the different levels of categorical explanatory variables within statistical models. Quasi-variances can be presented alongside parameter estimates to enable readers to assess differences between any combinations of parameter estimates for a categorical explanatory variable. The approach is beneficial because such comparisons are not usually possible without access to the full variance-covariance matrix for the estimates.
Using quasi-variance estimates addresses the reference category problem. The underlying idea was first proposed by Ridout but the technique was set out by
David Firth and Renee Menezes. The suitability of this technique for social science data analysis has been demonstrated.
See also
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Regression model
*
Generalized linear model
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a ''link function'' and by ...
*
Explanatory variable
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function ...
References
{{Reflist
External links
An extended set of resources with examples in
Stata
Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose Statistics, statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers ...
and
SPSS
SPSS Statistics is a statistical software suite developed by IBM for data management, advanced analytics, multivariate analysis, business intelligence, and criminal investigation. Long produced by SPSS Inc., it was acquired by IBM in 2009. Versi ...
are als
available
Statistical deviation and dispersion