What does FIML mean in MATHEMATICS

FIML is an estimation technique in statistics that allows for missing data in computations. It can take into account all available information when making maximum likelihood estimates, even observations that are partially or entirely missing. This makes it an advantageous technique for situations where data sets contain missing values or have a large number of variables.

Yes, FIML can be used with both categorical and continuous data. It offers the advantage of being able to handle both types of variables on equal footing, making it a useful tool for researchers who need to analyze data gathered from diverse sources.

FIML is most commonly used in longitudinal studies and psychometric testing. However, its application could extend beyond these two areas because it works well with any situation where some values are missing from a dataset due to either random or systematic errors.

By using all available information, including those cases that are partially or completely not observed in the data set, FIML eliminates selection bias from the evaluation process. This ensures estimates are more accurate than they would be if selection bias were present in the analysis.

While both techniques assume that there exist underlying probability distributions which generate the observed outcomes, CML allows for embedded parameters which change over time while keeping all other parameters constant. On the other hand, FIML allows for parameters to vary simultaneously over time without holding constant any previous set of parameters. Therefore, whereas MLE results may sometimes contain bias due to ignoring certain conditions present at different points in time, FIML takes these conditions into account and compensates accordingly to reduce bias as much as possible.

Multiple imputation may still be a viable option depending on your particular research context since it does not require your dataset to satisfy the assumptions necessary for maximum likelihood estimation techniques such as FIML. Furthermore, multiple imputation may result in slightly lower bias compared to other methods when applied correctly and therefore may be preferable when dealing with datasets containing lots of missing values.

Your dataset must meet three major criteria before you can use FIML; firstly, observations within a dataset must adhere to the normality assumption; secondly, variances across observations must all be equal; finally, coefficients forming linear models should remain unchanged across each observation period.