# Why does longitudinal models work for uneven measurements per subject? Analysis for uneven measurements

Again, today I heard about the same thing. That is, in any lab experiment, if some subjects (ex: medical patients) have 2 observations, some have 3 observations, some have 4 observations.... apparently anova/hypothesis tests dont work .... but longitudinal regression apparently can still work.

Why? Can someone explain? Why can longitudinal model work for uneven measurements for patients.... but other analysis does not? Is there some statistical assumptions here that affect this?

Which longitudinal model?

Any model that attempts to model repeated measures is going to be a "longitudinal model" of some sort or other. One common model for such data is the multilevel model. Someone else can (if they like) get more into the math but, basically, these models don't assume that there are an equal number of observations or that they are equally spaced.

It would be better to ask why other models can NOT do this. For instance, RM ANOVA has problems with data like this.

OTOH, you can look at one outcome point in a cross-sectional way, but this ignores a lot of the data, is less powerful (in the statistical sense) and can answer fewer questions.

• Thx! Why in repeat measures anova there is such a requirement for equal number of observations?? Sep 28 at 0:38
• I may have known the mathematical reason at one time, but I have forgotten. Some of the more mathematically expert users here may know. But you should probably ask a different question (or search for it). Sep 28 at 9:55

You can use "incomplete" data (data were some participants provide fewer data points than others) also with wide-format procedures such as RM ANOVA (i.e., by using multiple imputation for observations with "missing" time points). Multilevel models for (long-format) longitudinal data implicitly use all available data (including "incomplete" cases) by employing maximum likelihood estimation (sometimes referred to as "full information maximum likelihood" or FIML with missing data).

• FIML (generalized least squares, mixed effects models, Bayesian models, etc.) makes the right connections between correlation observations to properly handle data gaps. This allows one to assume missing at random (missingness is completely random after accounting for previous responses) but not have to assume missing completely at random. Non-FIML methods assume missing completely at random. Sep 28 at 12:43