psychometrika—vol. 82, no. 3, 846–870
MODELING LEARNING IN DOUBLY MULTILEVEL BINARY LONGITUDINAL DATA
USING GENERALIZED LINEAR MIXED MODELS: AN APPLICATION TO MEASURING
AND EXPLAINING WORD LEARNING
Sun-Joo Cho and Amanda P. Goodwin
VANDERBILT UNIVERSITY’S PEABODY COLLEGE
When word learning is supported by instruction in experimental studies for adolescents, word knowl-
edge outcomes tend to be collected from complex data structure, such as multiple aspects of word knowl-
edge, multilevel reader data, multilevel item data, longitudinal design, and multiple groups. This study
illustrates how generalized linear mixed models can be used to measure and explain word learning for
data having such complexity. Results from this application provide deeper understanding of word knowl-
edge than could be attained from simpler models and show that word knowledge is multidimensional and
depends on word characteristics and instructional contexts.
Key words: binary longitudinal data, doubly multilevel data, generalized linear mixed models, learning,
psycholinguistic data, word learning.
Reading theories suggest that the more students know about words, the easier it is to compre-
hend text (Perfetti, 2007). Yet word learning is a monumental task because readers can encounter
about 180,000 different words in academic texts (Graves, 2007). While many of these words are
learned through exposure like through speech and reading, many must be taught via vocabulary
instruction (Graves, 2007). Therefore, word learning is a primary focus for reading researchers.
Word learning is difﬁcult to study because words vary in how easy or hard they are to learn
due to different word characteristics (Nagy, Anderson, & Herman, 1987) and readers also differ in
how easily they learn words (Perfetti, 2007). For example, a word like statistician would be harder
than a word like mathematician because it is less frequent and is made up of less frequent parts
that are less likely to be recognized like statistic versus math (Schreuder & Baayan, 1995). Also,
as documented by the Matthew effect (Stanovich, 1986), both words would be harder to learn
for a reader with less vocabulary knowledge, like a child who did not know the term math.This
is because children learn words by linking new lexical representations to lexical representations
already in their lexicon (Perfetti, 2007). English language learners, who are learning English
as a second language and therefore have fewer English lexical representations, may therefore
have additional challenges learning English words. Instruction also plays a role, with research
suggesting that teaching students about morphological principles, like how to use afﬁxes and root
words to ﬁgure out the meanings of words, can support word learning (Goodwin & Ahn, 2010;
2013). Overall, reading researchers face multiple sources of variability when considering word
learning; and reading researchers need statistical models that can take into account the complex
nature of word learning.
In this article, we present a case study that highlights the complexity of word learning.
This case study examines the word learning of 202 adolescents who are part of an intervention
aimed at building vocabulary knowledge and reading skills. The students differ in word reading,
Correspondence should be made to Sun-Joo Cho, Vanderbilt University’s Peabody College, Nashville, TN, USA.
Email: firstname.lastname@example.org. http://www.vanderbilt.edu/psychological_sciences/bio/sun-joo-cho
© 2016 The Psychometric Society