spurious variable

Examples of spurious variable in the following topics:

• Some Pitfalls: Estimability, Multicollinearity, and Extrapolation

  • A key issue seldom considered in depth is that of choice of explanatory variables.
  • There are several examples of fairly silly proxy variables in research - for example, using habitat variables to "describe" badger densities.
  • In a study on factors affecting unfriendliness/aggression in pet dogs, the fact that their chosen explanatory variables explained a mere 7% of the variability should have prompted the authors to consider other variables, such as the behavioral characteristics of the owners.
  • Despite the fact that automated stepwise procedures for fitting multiple regression were discredited years ago, they are still widely used and continue to produce overfitted models containing various spurious variables.
  • Examine how the improper choice of explanatory variables, the presence of multicollinearity between variables, and extrapolation of poor quality can negatively effect the results of a multiple linear regression.

• Correlation and Causation

  • Causation refers to a relationship between two (or more) variables where one variable causes the other.
  • change in the independent variable must precede change in the dependent variable in time
  • it must be shown that a different (third) variable is not causing the change in the two variables of interest (a.k.a., spurious correlation)
  • It is often the case that correlations between variables are found but the relationship turns out to be spurious.
  • Thus, the correlation between ice cream consumption and crime is spurious.

• Experimental Design

  • Other variables, which may not be readily obvious, may interfere with the experimental design.
  • To control for nuisance variables, researchers institute control checks as additional measures.
  • One of the most important requirements of experimental research designs is the necessity of eliminating the effects of spurious, intervening, and antecedent variables.
  • $Z$ is said to be a spurious variable and must be controlled for.
  • The same is true for intervening variables (a variable in between the supposed cause ($X$) and the effect ($Y$)), and anteceding variables (a variable prior to the supposed cause ($X$) that is the true cause).

• Stepwise Regression

  • Forward selection involves starting with no variables in the model, testing the addition of each variable using a chosen model comparison criterion, adding the variable (if any) that improves the model the most, and repeating this process until none improves the model.
  • Backward elimination involves starting with all candidate variables, testing the deletion of each variable using a chosen model comparison criterion, deleting the variable (if any) that improves the model the most by being deleted, and repeating this process until no further improvement is possible.
  • This problem can be mitigated if the criterion for adding (or deleting) a variable is stiff enough.
  • The key line in the sand is at what can be thought of as the Bonferroni point: namely how significant the best spurious variable should be based on chance alone.
  • Unfortunately, this means that many variables which actually carry signal will not be included.

• Confounding

  • A confounding variable is an extraneous variable in a statistical model that correlates with both the dependent variable and the independent variable.
  • A confounding variable is an extraneous variable in a statistical model that correlates (positively or negatively) with both the dependent variable and the independent variable.
  • A perceived relationship between an independent variable and a dependent variable that has been misestimated due to the failure to account for a confounding factor is termed a spurious relationship, and the presence of misestimation for this reason is termed omitted-variable bias.
  • However, a more likely explanation is that the relationship between ice cream consumption and drowning is spurious and that a third, confounding, variable (the season) influences both variables: during the summer, warmer temperatures lead to increased ice cream consumption as well as more people swimming and, thus, more drowning deaths.
  • Break down why confounding variables may lead to bias and spurious relationships and what can be done to avoid these phenomenons.

• Analyzing Data and Drawing Conclusions

  • In this case, it's because of a third variable: temperature.
  • Regression analyses measure relationships between dependent and independent variables, taking the existence of unknown parameters into account.
  • More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.
  • Qualitative data can involve coding--that is, key concepts and variables are assigned a shorthand, and the data gathered is broken down into those concepts or variables .
  • It is important to remember, however, that correlation does not imply causation; in other words, just because variables change at a proportional rate, it does not follow that one variable influences the other .

• Aliasing

  • Figure 4.9: A sinusoid sampled at less than the Nyquist frequency gives rise to spurious periodicities.

• Explanatory and response variables

  • If we suspect poverty might affect spending in a county, then poverty is the explanatory variable and federal spending is the response variable in the relationship.
  • Sometimes the explanatory variable is called the independent variable and the response variable is called the dependent variable.
  • If there are many variables, it may be possible to consider a number of them as explanatory variables.
  • The explanatory variable might affect response variable.
  • In some cases, there is no explanatory or response variable.

• Variables

  • In this case, the variable is "type of antidepressant. " When a variable is manipulated by an experimenter, it is called an independent variable.
  • An important distinction between variables is between qualitative variables and quantitative variables.
  • Qualitative variables are sometimes referred to as categorical variables.
  • Quantitative variables are those variables that are measured in terms of numbers.
  • The variable "type of supplement" is a qualitative variable; there is nothing quantitative about it.

• Types of Variables

  • Numeric variables have values that describe a measurable quantity as a number, like "how many" or "how much. " Therefore, numeric variables are quantitative variables.
  • A continuous variable is a numeric variable.
  • A discrete variable is a numeric variable.
  • An ordinal variable is a categorical variable.
  • A nominal variable is a categorical variable.