# Mixed-Effect Modeling using MATLAB

Linear Mixed-Effect (LME) Models are generalizations of linear regression models for data that is collected and summarized in groups. Linear Mixed- Effects models offer a flexible framework for analyzing grouped data while accounting for the within-group correlation often present in such data.

This example illustrates how to fit basic hierarchical or multilevel LME models.

Copyright (c) 2014, MathWorks, Inc.

## Contents

- Description of the Data
- Load Data
- Preprocess Data
- Fit a linear model and visualize the Gross State Product by region
- Visualize data and fitted model
- Fit separate linear models per group and visualize intervals of parameters
- Fit a single linear model with dummy variables for each state
- Fit a random intercept model
- Fit a random intercept and slope model
- Compare random slope and intercept models using Likelihood Ratio Test
- Fit Mixed-Effect models using matrix notation
- Forecast state GDP

## Description of the Data

This dataset consists of annual observations of 48 Continental U.S. States, over the period 1970–86 (17 years). This data set was provided by Munnell (1990)

**GDP:**Gross Domestic Product by state (formerly Gross State Product)**STATE:**Categorical variable indicating the state**YR:**Year the GDP value was recorded

Reference:

`Munnell AH (1990). Why Has Productivity Growth Declined? Productivity and Public Investment.” New England Economic Review``Econometric Analysis of Panel Data, 5th Edition, Badi H. Baltagi`

## Load Data

```
clear, clc, close all
loadPublicData
```

If you don't have the data. You can download the Zip file from here.

## Preprocess Data

Convert STATE, YR and REGION to categorical, In Matlab 2021, its appear as a default that you will get it as a categorical

```
publicdata.STATE = categorical(publicdata.STATE);
% Compute log(GDP)
```

publicdata.log_GDP = log(publicdata.GDP);
publicdata.GDP = [];

## Fit a linear model and visualize the Gross State Product by region

The formula is

\( log\_GDP_i = \beta_0 + \beta_1 YR_i + \epsilon_i \)
## Comments