Comparing Coefficients

One of the limitations of the comparisons we have relied on here is that differences in consistency of findings related to violent versus nonviolent offending may occur if there is more measurement error in one or the other. In some of our papers, we have used techniques to compare coefficients across models (e.g., Savage et al., 2014), and these techniques do make adjustments for standard errors, but this is not completely adequate to address the problem of measurement error specifically. Thus, using the other methods recommended here is important.

Modee “Overspecification”

We frequently encountered what we have referred to as model “overspecification.” The most egregious form, for our needs, involves the simultaneous inclusion of multiple variables that measure the same construct in the model. Because most regression estimates partial out unique variance of independent variables from “common variance,” effect estimates in these models are conservative, and this may result in a type II error. Furthermore, the interpretation of coefficients can become very narrowly circumscribed. So, for example, in Chapter 8 where studies of abuse included physical abuse, sexual abuse and neglect in the same model, the interpretation of the partial coefficient for sexual abuse is “the association between sexual abuse and violent behavior, after already accounting for the association between physical abuse, neglect, other control variables and violence.” If most of the sexually abused participants were also physically abused or neglected, as may be the case, the estimate is not likely to be very reliable. If part of the effect of sexual abuse on future violence by victims is due to physical force used on the victim, the effect of sexual abuse is likely to be underestimated. In theory, the partial coefficient is only reflecting the sexual component of the abuse. This problem was also seen in Chapter 10 on communities. For our purposes, the estimate is likely to be biased in a downward direction, and in some cases, the inclusion of the extra variables may result in the partial coefficient estimate failing to achieve statistical significance (e.g., Allen, 1997). There are ways to use progressive models to look at changes in R2 as variables are entered and removed, but few authors follow this procedure. Model specification is a very important matter. Analysts should take care not to “control out” factors that have considerable overlap with their construct of interest.

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