Longitudinal Analysis

Longitudinal Analysis

Repeated measures and longitudinal data offer rich possibilities for business insights and research advances. Whether you have experimental data, need to monitor simple time trends, or have complex data with unknown time trends, Elkhart Group Ltd. is ready to use modern analytics to help you understand your data and answer your questions with confidence. Continuous or categorical variables, missing data, or nonrandom study dropout, our statistical consultants are ready to tackle even the most complex questions and give you simple answers and graphs to understand and take action on your results.


Experiments often collected repeated measures throughout the study, and require special analyses that account for non independence of each assessment. Our statistical consultants can help you take advantage of all the measures in an experiment by using repeated measures ANOVA or more modern mixed models for your data. If you are collecting physiological or biological data, we can use area under the curve (AUC) analyses to compute the total amount of a particular analyte output during the course of the experiment.

Longitudinal Analysis

Whether you are monitoring trends in attitudes toward your company's products, exploring health behaviors after a heart attack, or looking at fluctuations in employment and marriage, we can help you analyze and interpret your longitudinal data. Our statistical consultants can use mixed effects models or latent growth models to capture individual differences in starting points and growth or change over time. We can help detect and explore nonlinear time trends, and account for residual autocorrelation or dependence in your data.

For complex longitudinal categorical and count data, we can help you setup mixed models to test for significant effects, and also help you convert back to interpretable metrics, like changes in the probability of an event occurring. For rare events or models too complex for classical statistics, we can code hierarchical Bayesian models

. Longitudinal Expected Means with 95% Confidence Bars and P-values

Trajectory Analysis

Not all individuals follow the same trajectories. Our statistical consultants can use latent class analysis and growth mixture models to answer hypotheses that that there are distinct classes of people with their own trajectories over time, whether you have discrete time measures or a truly continuous time assessment. We will partner with you to compare results from models specifying different numbers of distinct classes and explain the assumptions of each model so that you find a solution that both makes theoretical sense and fits the data well.

Suppose a researcher studied depressive symptoms and measured them at four time points in cancer patients after diagnosis. Traditional latent growth models and mixed effects models for longitudinal and repeated measures data assume that everyone has the same general trajectory. Our analysts can use growth mixture models or latent class analyses to explore whether there are distinct trends in your data. The results of such an analysis on a sample dataset finds four classes with the means of each class at each time point shown below. The pattern is that patients in Class 4 are stable and high in depressive symptoms, Class 2 are stable and low in depressive symptoms, and Classes 1 & 3 start low and high, respectively, and then switch later on, representing a late reactivity and a recovery trajectory.

Plots of the raw data, separated by group after the growth mixture model identified unique trajectories are shown here.

Trajectory Graph Example

Intensive Longitudinal Designs

Intensive data collection such as ecological momentary assessment (EMA) where there are many observations for each participant often may not follow simple time trends. We can use piecewise or spline models for time to fit complex time trends. We also know that data may be cyclical or exhibit unknown time trends. Our statistical consultants can use generalized additive mixed models (GAMMs) to estimate models that flexibly fit time trends without having to specify the functional form.

Graph of Results from Generalized Additive Mixed Model with 95% Confidence Lines

Multiple Processes and Parallel Growth Models

Although most analyses focus on one or two outcome variables, some questions require assessing the trajectories of multiple outcomes simultaneously. For example, do individuals' slopes of reaction times to a short puzzle task predict cognitive performance and decline over a five year period? In newly cohabiting couples, do brand preferences change together, or does one partner influence the other? Should advertising be targeted at both members of the couple or is targeting one member sufficient to eventually change the other? At Elkhart Group, we are committed to answering your questions with straightforward answers. Our statistical consultants can design parallel growth models to examine whether trajectories predict each other or move in tandem. We can analyze your data to answer whether multiple processes move in synchrony or co-regulate each other.

Dropout and Missing Data

In longitudinal studies, participants are lost to follow up and missing data is the rule, not the exception. If you have intermittent missing data, our statistical consultants can use multilevel multiple imputation or full information maximum likelihood. If your data may be missing not at random, we can implement pattern mixture models, and shared parameter or joint models where longitudinal trajectories and time until study dropout is simultaneously estimated to account for non random dropout.

Service Levels

Premier: Our most bespoke offering. Let our consultants create solutions and reports that turn your data into strategic insight.

Academic: For accredited, not-for-profit universities. From methods write up assistance to advanced model analysis, we are experienced researchers who enjoy scientific discovery.

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