  Intensive longitudinal (IL) data are increasingly prevalent in psychological
science, coinciding with technological advancements that make it simple to
deploy study designs such as daily diary and ecological momentary assessments.
IL data are characterized by a rapid rate of data collection (1+ collections
per day), over a period of time, allowing for the capture of the dynamics that
underlie psychological and behavioral processes. One powerful framework for
analyzing IL data is state-space modeling, where observed variables are
considered measurements for underlying states (i.e., latent variables) that
change together over time. However, state-space modeling has typically relied
on continuous measurements, whereas psychological data often comes in the form
of ordinal measurements such as Likert scale items. In this manuscript, we
develop a general estimating approach for state-space models with ordinal
measurements, specifically focusing on a graded response model for Likert scale
items. We evaluate the performance of our model and estimator against that of
the commonly used ``linear approximation'' model, which treats ordinal
measurements as though they are continuous. We find that our model resulted in
unbiased estimates of the state dynamics, while the linear approximation
resulted in strongly biased estimates of the state dynamics
