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Accounting for Projection Bias in Models of Delinquent Peer Influence: The Utility and Limits of Latent Variable Approaches

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Abstract

Objectives

Projection effects have been shown to bias respondent perceptions of peer delinquency, but network data required to measure peer delinquency directly are unavailable in most existing datasets. Some researchers have therefore attempted to adjust perceived peer behavior measures for bias via latent variable modeling techniques. The present study tested whether such adjustments render perceived peer coefficients equal to direct peer coefficients, using original data collected from 538 young adults (269 dyads).

Methods

After first replicating projection effects in our own data and examining the degree to which measures of personal, perceived peer, and direct peer violence represent empirically distinct constructs, we compared coefficients derived from two alternative models of personal violence. The first model included an error-adjusted latent measure of perceived peer violence as a predictor, whereas the second substituted a latent measure of directly-assessed, peer-reported violence.

Results

Results suggest that personal, perceived peer, and direct peer measures each reflect fundamentally separate constructs, but call into question whether latent variable techniques used by prior researchers to correct for respondent bias are capable of rendering perceived peer coefficients equal to direct peer coefficients.

Conclusions

Research cannot bypass the collection of direct peer delinquency measures via latent variable modeling adjustments to perceived peer measures, nor should models of deviance view perceived peer and direct peer measures as alternative measures of the same underlying construct. Rather, theories of peer influence should elaborate and test models that simultaneously include both peer measures and, further, should attempt to identify those factors that account for currently unexplained variance in perceptions of peer behavior.

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Notes

  1. While some studies “have used a residual score approach to compute discrepancy scores” rather than a difference-score approach, some research has used both methods simultaneously, “yielding discrepancy scores that were nearly identical (i.e., r’s > .95) to one another and producing an identical pattern of results” (Prinstein and Wang 2005:297–298).

  2. Models run via fully-weighted least squares estimation failed to converge, likely as a result of our models’ complexity and limited sample size.

  3. One reviewer suggested that we consider an alternative strategy involving transforming our indicator items to reduce skew and estimating our models via the traditional maximum likelihood algorithm. We therefore ran an alternative set of models in which we (a) computed the natural log of each of our skewed indicator items; (b) computed traditional Pearson correlations; and (c) estimated all measurement and structural equation models via the maximum likelihood algorithm. Substantive results (available upon request) were identical to those presented herein, with one minor exception, noted below, that does not change our conclusions in any way. Because conclusions remained the same, and for the reasons discussed in “Estimation Method”, we present DWLS results using polychoric correlations.

  4. For purposes of comparison, the three-factor model presented in Fig. 2 fit the data better than did (a) a one-factor model (Δχ2 = 525.10, df = 7, p < .05); (b) a two-factor model in which perceived and direct peer behavior loaded on one factor (Δχ2 = 322.98, df = 6, p < .05); (c) a two-factor model in which personal behavior and perceived peer behavior loaded on one factor (Δχ2 = 182.81, df = 6, p < .05); and (d) a three-factor model omitting error correlation estimates of projection (Δχ2 = 39.90, df = 4, p < .05). Respectively, in comparison to the Fig. 2 model’s RMSEA of .026, the above alternatives yielded poorer fits of .191, .153, .115, and .058.

  5. The corresponding coefficient from our maximum-likelihood model did achieve statistical significance, but the gap between Figs. 3 and 4 coefficients when using maximum-likelihood estimation was similar to the gap presented in Figs. 3 and 4. Thus, conclusions about the research questions that we discuss at the outset were identical to those drawn from DWLS estimates, whose standard errors are likely to be more valid in light of the methodological literature we cite in “Estimation Method”.

  6. Given that our alternative models have used the same sample with different measures of peer violence rather than the same measures of peer violence with different samples, it is not appropriate to compare the coefficients of alternative models via the Paternoster et al. (1998) formula.

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Acknowledgments

We thank Robert Agnew, Tim Brezina, Ginger Lockhart, Michelle E. Manasse and Jacob T. N. Young for suggestions on a prior version of this manuscript. Preparation of this manuscript was funded in part by NIH Training Grant #T32 MH 018387. A previous version of this manuscript was presented at the 2012 Annual Meetings of the American Society of Criminology.

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Authors and Affiliations

  1. Department of Sociology, University of New Hampshire, 20 Academic Way, Horton Social Science Center, Durham, NH, 03824, USA

    Cesar J. Rebellon

  2. School of Psychology, Murdoch University, Murdoch, WA, Australia

    Kathryn L. Modecki

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  1. Cesar J. Rebellon
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Correspondence to Cesar J. Rebellon.

Appendix

Appendix

See Table 2.

Table 2 Measurement model
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Rebellon, C.J., Modecki, K.L. Accounting for Projection Bias in Models of Delinquent Peer Influence: The Utility and Limits of Latent Variable Approaches. J Quant Criminol 30, 163–186 (2014). https://doi.org/10.1007/s10940-013-9199-9

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