Abstract
School counselors are the primary facilitators of college transition for many students, yet little is known about their influence on college-going behavior. Analyzing data from the Educational Longitudinal Study of 2002, this study employs coarsened exact matching and multilevel modeling to examine the effects of student-counselor visits on postsecondary enrollment, as well as determine whether the effects of such visits vary by socioeconomic background. Results suggest that visiting a counselor for college entrance information has a positive and significant influence on students’ likelihood of postsecondary enrollment, and that counseling-related effects are greatest for students with low socioeconomic status.
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Notes
As explained below in the Analytic Design subsection, I employed full information maximum likelihood estimation, which allowed for the incorporation of all cases with data on at least one variable included in my model.
See discussion on coarsened exact matching in the Analytic Design subsection.
Socioeconomic status is measured by a composite variable featured in ELS:2002/2006 and other NCES large-scale studies, and that is based on five equally weighted components of information provided by students’ parents via ELS’s base year (2002) parent questionnaire: father’s education; mother’s education; family income; father’s occupation; and mother’s occupation. The SES composite variable is continuous, with higher calculated student SES scores assigned to students of higher socioeconomic status.
Scores are from a math and reading standardized assessment administered by NCES during the base year (2002) of the ELS survey.
In contrast, PSM relies on model based procedures (usually a logit or probit function) and matches units that share similar scores, but that may also differ considerably one or more covariates included in the model—since units are matched on predicted probabilities of treatment, and not on their actual traits. PSM may also produce scores that incorporate observations existing within a region or sample space of extrapolation (i.e., propensity scores may be tainted by treated observations that do not contain a control counterpart, and vice versa). In both instances, estimates of a treatment effect are likely to be biased (Battistin and Chesher 2004).
Other matching methods that are not MIB (e.g., PSM and MD) are designed to address a different and less concerning problem, namely large variance. However, attempts to maximize efficiency (via ensuring an adequately sized sample) often preclude users from achieving a desired level of covariate balance. This tradeoff is unfavorable, given that sample sizes are sufficiently large in many observational studies, particularly those which are conducive to matching, and also given that “it is generally not wise to obtain a very precise estimate of a drastically wrong quantity” (Rubin 2006, p. 11). For example, in empirical applications, researchers often have to tweak and rerun PSM and Mahalanobis models to produce an accepted level of balance; however, model specifications that improve balance on one variable may reduce balance on another, leaving researchers guessing as to which matching algorithm produces the least bias. In contrast, CEM’s non-parametric properties enable researchers to define the value space within which units are to be matched—for each covariate separately and without influencing balance in any of the other included covariates—in effect, producing greater global balance, and consequently, less bias.
However, since PSM and Mahalanobis methods are model dependent (in that they reduce a covariate set from k-dimensional space to a more restricted space defined by a propensity score or Mahalanobis distance) causal inference is justifiable only under a certain set of unverifiable assumptions, namely that one’s model is correctly specified, of a correct functional form, and that propensity scores are constant across X (Iacus and King 2012). These assumptions often impose and insurmountable burden of proof upon a researcher who is attempting to defend the quasi-experimental design of his or her study.
It is important to note that while the normal distribution plays an essential role in maximum likelihood estimation, FIML is quite robust in the presence of non-normal data (Enders 2001). However, in models with highly discrete dependent variables, such as the one used in this study, FIML may lead to bias standard errors. As a corrective measure, and based on the recommendation of Enders (Enders 2010), I incorporate a robust estimator (White 1980) into my analysis.
Put more explicitly, and to utilize an example from Peugh and Enders (2004), suppose our objective is to estimate a covariance matrix and vector of means used to provide regression estimates. In order to do so, the FIML estimator maximizes the following log-likelihood function for each observation in a particular sample:
$$log L_{i}= K_{i}- \frac{1}{2} \hbox {log}|\Upsigma_{i}| - \frac{1}{2}(x_{i}-\mu_{i})^\top \Upsigma^{-1}(x_{i}-\mu_{i}) $$(2)where K i is a constant indicating the number of complete data points for observation i, x i is the observed data for observation i; μ i and \(\Upsigma_{i}\) are parameter estimates for the mean vector and covariance matrix, respectively, and the size of which are determined by the number of variables on which a particular observation has complete data, as denoted by the subscripts i in the above equation. The likelihood functions for each observation are then summed across the entire sample and maximized according to the following:
$$log L(\mu,\Upsigma)=\sum^{N}_{i=1}logL_{i} $$(3)Additionally, and perhaps not quite as apparent, all cases, even those with incomplete data, contribute to the estimation of every parameter in the model (Peugh and Enders 2004). For example, in a trivariate model, where X and Y predict Z, observations with X and Y, but not Z, still contribute to the estimation of Z, since the estimation of Z is, in part, a function of the covariance between X and Y. In other words, likely values of Z are implied by observed values of X and Y; so, even if observations are missing values on Z, their values of X and Y can still contribute to the estimation of Z, while also improving the precision and efficiency of the Z estimate (since N increases and more information is incorporated into the model). This is conceptually analogous to what occurs during multiple imputation; however, data are not actually imputed in FIML estimation, and so there is no risk of estimating a model on the basis of unlikely values that could have been produced via an improperly specified imputation model.
The vertical arrows in each graph indicate at which SES “score” the effect of student counselor visits becomes statistically indistinguishable from zero.
Confidence intervals calculated for the predicted probabilities confirm this finding.
When discussing results generated by a multinomial model, or other models with a dichotomous or categorical outcome, it is important not to confuse likelihood with probability. For example, and in the context of this study, a significant interaction between student-counselor visits and socioeconomic status indicated varying effect sizes with respect to the odds of one outcome compared to another—for example, four-year enrollment versus no enrollment—but it does not necessarily indicate varying effect sizes with respect to the probability of four-year enrollment overall.
Additionally, and although not pictured in Fig. 3 (to preserve clarity of presentation), it is important to note that confidence intervals for predicted probabilities among counselees and non-counselees begin to overlap between the 35th and 40th percentiles of SES “score”, suggesting no significant effects of counselor-visits at higher ends of the socioeconomic scale—at least when it came to the probability of enrolling in postsecondary education anywhere.
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This research was supported by a grant from the American Educational Research Association which receives funds for its “AERA Grants Program” from the National Science Foundation under Grant #DRL-0941014. Opinions reflect those of the author and do not necessarily reflect those of the granting agencies. The author gratefully acknowledges the support and suggestions of James Hearn, Erik Ness, Manuel González Canché, Sheila Slaughter, Michael Trivette, the editor, anonymous reviewers and the Abington School District (PA).
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Belasco, A.S. Creating College Opportunity: School Counselors and Their Influence on Postsecondary Enrollment. Res High Educ 54, 781–804 (2013). https://doi.org/10.1007/s11162-013-9297-4
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DOI: https://doi.org/10.1007/s11162-013-9297-4