Estimating competitive and other relationships among plants is difficult but important. Common estimation methods involve modeling target plant variables (e.g. growth, survival) as functions of neighbor variables (e.g. density, biomass) after measuring the variables in plots or neighborhoods of individual targets. It can be important to include abiotic (e.g. disturbances, nutrients) variables in the models to control for their effects, because these variables can vary appreciably across plots, plant neighborhoods and time. But deciding which variables to measure and include is difficult owing to ignorance about which variables affect which plants. Variables that affect only neighbors should be omitted because including them risks masking neighbor effects. Conversely, omitting variables that affect only targets increases uncertainty, and omitting variables that affect both neighbors and targets causes omitted variable bias. Concerning the direction of bias, typical models will underestimate competition intensity whenever omitted variables positively or negatively affect both neighbors and targets, and because different plants respond similarly to nutrients and a variety of other factors, we hypothesized omitted variables would usually cause underestimated competition.
Results/Conclusions
In example analyses, we show how instrumental variables models can use instruments, variables that affect targets only by affecting neighbors, to estimate and correct omitted variable bias with no knowledge of what the omitted variables even are. With experimental data, omitted variables sometimes caused underestimated competition intensity, and with observational data, omitted variables caused a competitive relationship to seem mutualistic. These results support our hypothesis that omitted variables tend to cause underestimated competition intensity, as do two recent observational studies where models underestimated competition. In addition to omitted variables, we show how measurement errors in neighbor variables can cause competition to seem weaker than it is. Unfortunately, with observational data, valid instruments are rare, so instrumental variables analysis is not a general-purpose solution to the omitted variables problem. With experimental data, treatment indicators are often valid instruments, so instrumental variables analysis seems more generally useful.