A Fixed Effects Panel Data Model: Mathematics Achievement in the U.S. Page: 1
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Fixed Effects Panel Data
A Fixed Effects Panel Data Model:
Mathematics Achievement in the U.S.Todd Sherron Jeff M. Allen
University of North TexasStatisucal models that combine cross section and time series data offer analysis and interpretation advantages over
separate cross section or time series data analyses (Mtys & Severstre, 1996). Time series and cross section
designs have not been commonplace in the research community until the last 25 years (Tieslau, 1999). In this
study, a fixed effects panel data model is applied to the National Education Longitudinal Study of 1988 (NELS:88)
data to determine if educational process variables, teacher emphasis, student self-concept. and socio-econormic status
can account for variance in student mathematical achievement. A model that includes seven independent variables
accounted for 25% of the variance in student mathematical achievement test score. The study provides educational
researchers with an applied model for panel data analysis.ime series and cross section designs have not
been commonplace in the research community
until the last 25 years (Tieslau, 1999). In fact.
the U.S. Department of Educations National Center
for Education Statistics (NCES) was not mandated to
"collect and disseminate statistics and other data related
to education in the Uruted States" until the Education
Amendments of 1974 (Public Law 93-380, Title V,
Section 501, amending Part A of the General
Education Provisions Act). Researchers commonly
have termed data that contains tme series and cross
secuon units to be panel or longitudinal data. In this
study, these terms are used interchangeable.
Essentially, panel data is a set of individuals who are
repeatedly sampled at different intervals in time, across
a multitude of cross sectional variables. The term
"individual" might be used loosely to imply a person,
a household, a school, school districts, firms, or a
geographical region. Figure 1 provides a typical Panel
data structure. Schools have been used to represent the
different "individuals". (Note: the individual unit could
just as well have been different schools within a
pamcular district, school districts within a state, or an
aggregate representation by state).
Researchers who are interested in understanding,
explaining, or predicting variation within longitudinal
data are faced with complex stochastic specifications.
The problem that occurs when measures exhibit two-
dimensional variation-variation across time and cross
section, in model specification. In other words,
researchers need to specify a model that can capture
individual differences in behavior across individuals
and/or through time for estimation and inference
purposes (Greene, 1997). In general, longitudinal
(panel) data sets contain a large number of cross-
section units and a relatvely small number of time-
series units.
The U.S. Department of Education began
collecting data in 1988 about critical transitions
experienced by students as they leave elementary
schools and progress through high school and into
Multiple Linear Regression Viewpoints. 2000. Vol. 26(1)postsecondary institutions or the work force. The
National Education Longitudinal Study of 1988
(NELS:88) contains data about educational processes
and outcomes pertaining to student learning, predictors
of dropping out, and school effects on students' access
to programs and equal opportunities to learn. The first
follow-up was conducted with the same students, their
teachers, and principals in 1990. The second follow
up survey was conducted in 1992, and the third in
1994. Data from NELS:88 will be used in this study
to determine if student perception of educational
process variables can account for the variance in
mathematical achievement.
Model Specification
When should a fixed effects or random effects
model be utilized? The answer to this question is
often debated. Some believe that it is dependent upon
the underlying cause in the model. For example, if the
individual effects are the result of a large number of
non-observable stochastic variables, then the random
effect interpretation is demanded. Others think the
decision rests on the nature of the sample - that is
when the sample is comprehensive or exhaustive, then
fixed effects models are the natural choice to enhance
the generalizability. On the contrary, if the sample
does not contain a large percent of the population then
the random effects model would be the model of
choice. According to Hasiao (1985), it is ultimately, "
up to the investigator to decide whether he wants to
make an inference with respect to population
characteristics or only with respect to effects that are in
the sample" (p. 131). It is unlikely that this debate
will ever be resolved per se, however, if the choice
between the two underlying methods is clear, then the
estimation method should be chosen accordingly.
However, if the choice is not clear, then the decision
should be based on the nature of the sample and
statistical evidence. For example, if the individual
effects are significant then this is a sign that a
significant component of the model is accounted for
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Sherron, Todd & Allen, Jeff M. A Fixed Effects Panel Data Model: Mathematics Achievement in the U.S., article, 2000; [Washington, D.C.]. (https://digital.library.unt.edu/ark:/67531/metadc31075/m1/1/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT College of Information.