Incremental validity is a type of validity that is used to determine whether a new psychometric assessment will increase the predictive ability beyond that provided by an existing method of assessment. [1] In other words, incremental validity seeks to determine whether the new assessment adds information that cannot be obtained with simpler, already existing methods. [2]
When an assessment is used with the purpose of predicting an outcome (perhaps another test score or some other behavioral measure), a new instrument must show that it is able to increase our knowledge or prediction of the outcome variable beyond what is already known based on existing instruments. [3]
A positive example may be a clinician who uses an interview technique as well as a specific questionnaire to determine if a patient has mental illness and has better success at determining mental illness than a clinician who uses the interview technique alone. Thus, the specific questionnaire would be considered incrementally valid. Because the questionnaire in conjunction with the interview produced more accurate determinations, and added information for the clinician, the questionnaire is incrementally valid.
Incremental validity is usually assessed using multiple regression methods. A regression model with other variables is fitted to the data first and then the focal variable is added to the model. A significant change in the R-square statistic (using an F-test to determine significance) is interpreted as an indication that the newly added variable offers significant additional predictive power for the dependent variable over variables previously included in the regression model. Recall that the R-square statistic in multiple regression reflects the percent of variance accounted for in the Y variable using all X variables. Thus, the change in R-square will reflect the percent of variance explained by the variable added to the model. The change in R-square is more appropriate than simply looking at the raw correlations because the raw correlations do not reflect the overlap of the newly introduced measure and the existing measures. [3]
An example this method is in the prediction of college grade point average (GPA) where high school GPA and admissions test scores (e.g., SAT, ACT) usually account for a large proportion of variance in college GPA. The use of admissions tests is supported by incremental validity evidence. For example, the pre-2000 SAT correlated .34 with freshman GPA while high school GPA correlated .36 with freshman GPA. [4] It might seem that both measures are strong predictors of freshman GPA, but in fact high school GPA and SAT scores are also strongly correlated, so we need to test for how much predictive power we get from the SAT when we account for high school GPA. The incremental validity is indicated by the change in R-square when high school GPA is included in the model. In this case, high school GPA accounts for 13% of the variance in freshman GPA and the combination of high school GPA plus SAT accounts for 20% of the variance in freshman GPA. Therefore, the SAT adds 7 percentage points to our predictive power. If this is significant and deemed an important improvement, then we can say that the SAT has incremental validity over using high school GPA alone to predict freshman GPA. Any new admissions criterion or test must add additional predictive power (incremental validity) in order to be useful in predicting college GPA when high school GPA and test scores are already known.
In statistics, the standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores.
Validity is the main extent to which a concept, conclusion, or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence described in greater detail below.
Factor analysis is a statistical method used to describe variability among observed, correlated variables in terms of a potentially lower number of unobserved variables called factors. For example, it is possible that variations in six observed variables mainly reflect the variations in two unobserved (underlying) variables. Factor analysis searches for such joint variations in response to unobserved latent variables. The observed variables are modelled as linear combinations of the potential factors plus "error" terms, hence factor analysis can be thought of as a special case of errors-in-variables models.
Linear trend estimation is a statistical technique used to analyze data patterns. Data patterns, or trends, occur when the information gathered tends to increase or decrease over time or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on a graph of data that models the general direction that the data is heading.
In psychometrics, predictive validity is the extent to which a score on a scale or test predicts scores on some criterion measure.
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable and one or more error-free independent variables. The most common form of regression analysis is linear regression, in which one finds the line that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line that minimizes the sum of squared differences between the true data and that line. For specific mathematical reasons, this allows the researcher to estimate the conditional expectation of the dependent variable when the independent variables take on a given set of values. Less common forms of regression use slightly different procedures to estimate alternative location parameters or estimate the conditional expectation across a broader collection of non-linear models.
In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.
Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.
In statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s).
In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Intuitively, IVs are used when an explanatory variable of interest is correlated with the error term (endogenous), in which case ordinary least squares and ANOVA give biased results. A valid instrument induces changes in the explanatory variable but has no independent effect on the dependent variable and is not correlated with the error term, allowing a researcher to uncover the causal effect of the explanatory variable on the dependent variable.
In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of regression, such as ordinary least squares, have favourable properties if their underlying assumptions are true, but can give misleading results otherwise. Robust regression methods are designed to limit the effect that violations of assumptions by the underlying data-generating process have on regression estimates.
In statistics, unit-weighted regression is a simplified and robust version of multiple regression analysis where only the intercept term is estimated. That is, it fits a model
In statistics, resampling is the creation of new samples based on one observed sample. Resampling methods are:
Multilevel models are statistical models of parameters that vary at more than one level. An example could be a model of student performance that contains measures for individual students as well as measures for classrooms within which the students are grouped. These models can be seen as generalizations of linear models, although they can also extend to non-linear models. These models became much more popular after sufficient computing power and software became available.
This entry will describe the proper narrow and technical meaning of "ecological validity" as proposed by Egon Brunswik as part of the Brunswik Lens Model, the relation of "ecological validity" in "representative design" of research, and will outline the common misuses of the "ecological validity." For a more detailed explanation, see Hammond (1998).
Omnibus tests are a kind of statistical test. They test whether the explained variance in a set of data is significantly greater than the unexplained variance, overall. One example is the F-test in the analysis of variance. There can be legitimate significant effects within a model even if the omnibus test is not significant. For instance, in a model with two independent variables, if only one variable exerts a significant effect on the dependent variable and the other does not, then the omnibus test may be non-significant. This fact does not affect the conclusions that may be drawn from the one significant variable. In order to test effects within an omnibus test, researchers often use contrasts.
In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.
In multivariate statistics, exploratory factor analysis (EFA) is a statistical method used to uncover the underlying structure of a relatively large set of variables. EFA is a technique within factor analysis whose overarching goal is to identify the underlying relationships between measured variables. It is commonly used by researchers when developing a scale and serves to identify a set of latent constructs underlying a battery of measured variables. It should be used when the researcher has no a priori hypothesis about factors or patterns of measured variables. Measured variables are any one of several attributes of people that may be observed and measured. Examples of measured variables could be the physical height, weight, and pulse rate of a human being. Usually, researchers would have a large number of measured variables, which are assumed to be related to a smaller number of "unobserved" factors. Researchers must carefully consider the number of measured variables to include in the analysis. EFA procedures are more accurate when each factor is represented by multiple measured variables in the analysis.
Measurement invariance or measurement equivalence is a statistical property of measurement that indicates that the same construct is being measured across some specified groups. For example, measurement invariance can be used to study whether a given measure is interpreted in a conceptually similar manner by respondents representing different genders or cultural backgrounds. Violations of measurement invariance may preclude meaningful interpretation of measurement data. Tests of measurement invariance are increasingly used in fields such as psychology to supplement evaluation of measurement quality rooted in classical test theory.
In statistics, linear regression is a statistical model which estimates the linear relationship between a scalar response and one or more explanatory variables. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. If the explanatory variables are measured with error then errors-in-variables models are required, also known as measurement error models.