Author Archives: Ian A. Silver

1. Introduction (PDF & R-Script) The prior entries in the current section reviewed the impact of altering the level of measurement of the dependent variable (Entry 13) and independent variable (Entry 14) on the magnitude of the estimated association. These entries demonstrated that the level of measurement reduced the magnitude of the estimated association betweenContinue reading “Entry 15: Level of Measurement Confounders, Colliders, Mediators, and Moderators”

Syntax

1. Introduction (PDF & R-Code) The independent variable – other terms include the treatment (0,1), predictor, or exogenous variable – is the mechanism in the population that we hypothesize causes changes in the dependent variable. That is, we believe that when a cases’ score on the independent variable increases or decreases, a cases’ score onContinue reading “Entry 14: Level of Measurement of the Independent Variable”

Just a warning, this is a long entry! Overall message, operationalize variables on a continuous scale when possible and consider the ramifications of transforming continuous distributions. 1.Introduction (PDF & R-Code)[i] I can see no place more fitting to start a discussion of Statistical Biases and Measurement than focusing on the measurement of our dependent variablesContinue reading “Entry 13: Level of Measurement of the Dependent Variable”

Introduction (PDF) Welcome to what I believe will be one of the most important sections of the Sources of Statistical Biases Series: Measurement. Besides the existence of confounders, I strongly believe that the measurement of a construct represents one of the largest sources of statistical bias in all scientific disciplines. This belief stems from theContinue reading “Statistical Biases and Measurement: Introduction”

Introduction (PDF & R-Code) The previous entries have focused on the biases that can exist when generating causal inferences through methodological and statistical approaches. I know it is considerably difficult for researchers trained in experimental methods – such as myself in criminology – to discern that causal inferences can be generated without randomly assigning participantsContinue reading “Entry 12: The Inclusion of Non-Causally Associated Constructs and Reverse Causal Specifications”

Introduction (PDF & R-Code) Generating causal inferences is a difficult process. We can run a true experiment (i.e., a randomized controlled trial), however that can be ethically concerning when randomizing certain treatments. Alternatively, we can develop a Directed Acyclic Graph (DAG) and reduce the influence of confounders and colliders on our association of interest. OrContinue reading “Entry 11: Instrumental Variables”

Introduction (PDF & R-Code) You might have the thought of: I know the constructs that can confound, mediate, or moderate the association I am interested in, and I am surely not going to include a collider as a covariate in my regression model! You also, like a great student of causal inference, have embraced theContinue reading “Entry 10: The Inclusion and Exclusion of Descendants”

PDF & R-Code A variety of techniques can be used to simulate linear associations between a continuous independent variable and a normal continuous dependent variable in R. I, however, rely on the lesser employed process of specifying linear directed equations. Briefly, a linear directed equation can be simply thought of as a regression formula but,Continue reading “Simulating Linear Associations with Normal Continuous Variables”

Introduction (PDF & R-Code) When I state “X is a cause of Y”, I am inherently implying that variation in X caused variation in Y. This statement, however, does not provide any indication of how X caused variation in Y. The how is just as important, if not more important, than knowing the causal association.Continue reading “Entry 9: The Inclusion and Exclusion of Mediating and Moderating Mechanisms”