While we have what we are calling ‘fixed’ effects, the distinguishing feature of the mixed model is the addition of this random component. All participants are providing multiple measurements. Question. Random effects in INLA are defined using a multivariate Gaussian distribution with zero mean and precision matrix \(\tau \Sigma\), where \(\tau\) is a generic precision parameter and \(\Sigma\) is a matrix that defines the dependence structure of the random effects and that may depend on further parameters. Mixed Models – Repeated Measures Introduction This specialized Mixed Models procedure analyzes results from repeated measures designs in which the outcome (response) is continuous and measured at fixed time points. When to choose mixed-effects models, how to determine fixed effects vs. random effects, and nested vs. crossed sampling designs. A O indicates the variable has a fixed intercept and not a random one. This is the effect you are interested in after accounting for random variability (hence, fixed). Because there was an improvement in between model 1 and model 2, but NO improvement between model 2 and model 3, we can proceed using the best fit model, nullmodel2, as our random effects structure for the rest of the analyses. 1Background Information. Mixed models in R For a start, we need to install the R package lme4 (Bates, Maechler & Bolker, 2012). xref Check correlation between intercept and slope (i.e. pf (20.58, df1 = 2, df2 = 10, lower.tail = FALSE) ## [1] 0.0002853299. As you can see by the p-values, while there is an improvement in fit from model 1 to model 2, model 3 did not explain more variance. Generalized linear mixed-effects models allow you to model more kinds of data, including binary responses and count data. A linear mixed effects model is a hierarchical model: it shares statistical strength across groups in order to improve inferences about any individual … The within-group errors are allowed to be correlatedand/or have unequal variances. Try out different structures, and use the anova function to find the best fitting random effects structure. In today’s lesson we’ll learn about linear mixed effects models (LMEM), which give us the power to account for multiple types of effects in a single model. 49 0 obj <> endobj Subject level variability is often a random effect. If an effect, such as a medical treatment, affects the population mean, it is fixed. Chapter 17: Mixed Effects Modeling. We can calculate the … In contrast, random effects are parameters that are themselves random variables. Linear Mixed Effects Models. When we do that we have to account for both within-person and across-person variability. Sometimes mixed-effects models are expressed as multilevel regression models (first level and grouping level models) that are fit simultaneously. Some technical detail: We can actually get the correct p-value for the mixed effects model from the above fixed effects model output. The core of mixed models is that they incorporate fixed and random effects. A mixed-effects model consists of fixed-effects and random-effects terms. ### Insert ggplot2 reference. As with all regression models, their purpose is to describe a response variable as a function of the predictor variables. Generic functions such as print, plot and summary have methods to show the results of the fit. Each data point consists of inputs of varying type—categorized into groups—and a real-valued output. A fixed effect is a parameterthat does not vary. Such data arise when working with longitudinal and other study designs in which multiple observations are made on each subject. The random effects structure reflects YOUR understanding of where to expect variance, and how nested data will interact with that variance. Some doctors’ patients may have a greater probability of recovery, and others may have a lower probability, even after we have accounted for the doctors’ experience and other meas… spline term. These are a few hypothetical random effects structures: The lmer package can be used for modeling, and the general syntax is as follows: ``` modelname <- lmer (dv ~ 1 + IV +(randomeffects), data = data.name, REML = FALSE). A random-intercepts model would adequately capture the two sources of variability mentioned above: the inter-subject variability in overall mean RT in the parameter \({\tau_{00}}^2\), and the trial-by-trial variability in the parameter \(\sigma^2\). For these models we do not need to worry about the assumptions from previous models, since these are very robust against all of them. b is a q -by-1 random-effects vector. Nested designs refer to the between-subject variable. Random intercepts models, where all responses in a group are additively shifted by a value that is specific to … The presence of … As with all regression models, their purpose is to describe a response variable as a function of the predictor variables. The core of mixed models is that they incorporatefixed and random effects. Psychology Definition of MIXED-EFFECTS MODEL: is used in the evaluation of variance where an experimenter assumes one or more variables as fixed and any further variables as random. Pizza study: Controlling for random effects of subject, pizza consumption, and effect of time on subject, all of which vary across participants. TheE-optimality of the following designs within the class of all proper and connected designs with givenb, k andv under mixed effects model are established. Let’s understand how the patients’ response can be estimated using both fixed effects model, and, mixed model which combines both fixed and the random effects. Results show that while pizza consumption and time are still significant main predictors, their interaction term did not reach significance. We can now conclude that after controlling for random effects, more pizza consumption does lead to improvements in mood over time, but there is no interaction with time. Let’s say that we are interested in examining the effect of pizza consumption on people’s moods. 0000002962 00000 n The general syntax is as follows: When there is a 1 before the line, you are accounting for random intercepts (varying baseline levels) in your variable. A single measure of residual variance can’t account for both. In summary, we have seen how two schools of thought treat fixed and random effects, discussed when to use fixed effects and when to use random effects in both frameworks, discussed the assumptions behind the models, and seen how to implement a mixed effect model in R. Fixed and random effect models still remain a bit mysterious, but I hope that this discussion cleared … - Expecting interaction such that more pizza over time predicts mood. This framework is widely applicable across numerous fields within the … Practical example: Logistic Mixed Effects Model with Interaction Term Daniel Lüdecke 2020-12-14. Check estimates for beta value – time has a significant effect, improvement in mood by about 1 point over time. Mixed effects models are useful when we have data with more than one source of random variability. Keep REML = FALSE. This function compares the fit of the model to see how fit has improved with additional items. Mixed-effects models are also called multilevel models or hierarchical models depending on the context. Lastly, the course goes over repeated-measures analysis as a special case of mixed-effect modeling. You can also visualize your data to see what fits. Random effects are factors whose levels were sampled randomly from a larger population about which we wish to generalize, but whose specific level values we actually don't care about. The researcher uses a mixed effects model to evaluate fixed and random effects together. With mixed models we’ve been thinking of coefficients as coming from a distribution (normal). The output of a mixed model will give you a list of explanatory values, estimates and confidence intervals of their effect sizes, p-values for each effect, and at least one measure of how well the model fits. 0 an object of class nlme representing the nonlinear mixed-effects model fit. Here, a double-blind, placebo-controlled clinical trial was conducted to determine whether an estrogen treatment reduces post-natal depression. Mixed-effects models for binary outcomes have been used, for example, to analyze the effectiveness of toenail infection treatments (Lesaffre and Spiessens2001) and to model union membership of young males (Vella and Verbeek1998). Below are some important terms to know for understanding the statistical concepts used in mixed models: Crossed designs refer to the within-subject variables (i.e. First, however, we need to specify the random effects term that best fits the data. 0000002885 00000 n Consider a case where you have data on several children where you have their age and height at different time points and you want to use age to predict height. That is why mixed-effects is the terminology preferred here. Linear Mixed Effects Models in R - Which is the better approach to build and compare models? With linear mixed effects models, we wish to model a linear relationship for data points with inputs of varying type, categorized into subgroups, and associated to a real-valued output. Random Effects. Hypotheses For Study Random effects: - “Subjects” will have their own intercepts. Dependent Variable: Purchase made (Yes/No) Independent Variable 1: Time spent (in store or on website) Note: (Data contain repeated measures over time for consumers) The null hypothesis, which is statistical lingo for what would happen if the treatment does nothing, is that there is no relationship between time spent and whether or not a purchase is made. Mixed effects, or simply mixed, models generally refer to a mixture of fixed and random effects. Mixed-effects models might include factors that are not necessarily multilevel or hierarchical, for example crossed factors. Random effect models are often hierarchical models. The subjects are sampled from … For example, we could say that \(\beta\) is … Check correlation of fixed effects – if too high, this may imply. In a linear mixed-effects model, responses from a subject are thought to be the sum (linear) of so-called fixed and random effects. An interactive version with Jupyter notebook is available here. In this example given below, the patients’ response to the vaccine is modelled as the probability of the vaccinated person falling sick due to Covid-19. Mixed-effects models is a more general term than the latter two. Here is some hypothetical data (code used to generate data can be found here): NOTE - This is a within-subjects study. 49 15 Such models are often called multilevel models. Model 3 – Including an interaction term between pizza consumption and time (pizza consumption varies over time). I first … X is an n -by- p fixed-effects design matrix. For example, a … Do they interact? 0000002185 00000 n the names of the variables, as character vector in the terms-argument. Another mixed effects model visualization Last week, I presented an analysis on the longitudinal development of intelligibility in children with cerebral palsy—that is, how well do strangers understand these children’s speech from 2 to 8 years old. Next, we fit a model with an interaction between the binomial and continuous variable. Because subjects start at. effects model!! The researcher has 4 fields where they can collect data. Random effects are factors whose levels were sampled randomly from a larger population about which we wish to generalize, but whose specific level values we actually don't care about. β is a p -by-1 fixed-effects vector. We are going to work in lme4, so load the package … While we have what we are calling ‘fixed’ effects, the distinguishing feature of the mixed model is the addition of this random component. - The slopes and intercepts of pizza consumption and time will be correlated (shared variance) Fixed effects: - Expecting there to be an overall main effect of pizza consumption over time. Fixed effects are plotted as intercepts to reflect the baseline level of your DV. 0000000884 00000 n Summary. Psychology Definition of MIXED-EFFECTS MODEL: is used in the evaluation of variance where an experimenter assumes one or more variables as fixed and any further variables as random. This kind of data appears when subjects are followed over time and measurements are collected at intervals. This generic function fits a nonlinear mixed-effects model in theformulation described in Lindstrom and Bates (1990) but allowing for nestedrandom effects. Download Rmd. While being connected to the internet, open R and type in: install.packages(“lme4”) Select a server close to you. no clustering. Lastly, the course goes over repeated-measures analysis as a special case of mixed-effect modeling. timepoint, condition, etc.). no clustering. Pizza study: The fixed effects are PIZZA consumption and TIME, because we’re interested in the effect of pizza consumption on MOOD, and if this effect varies over TIME. This vignette demonstrate how to use ggeffects to compute and plot marginal effects of a logistic regression model. The purpose of this workshop is to show the use of the mixed command in SPSS. The random effects have prior distributions, whereas the fixed … causing variance/variability in responses). Nathaniel E. Helwig (U of Minnesota) Linear Mixed-Effects Regression Updated 04-Jan-2017 : Slide 9 Sushmita Shrikanth. (See Random Effects.) Linear Mixed-Effects Models. Fixed-effects terms are usually the conventional linear regression part of the model. This concludes the tutorial on mixed effects models. Results show significant effects of both pizza consumption and time on mood! Random effects have a a very special meaning and allow us to use linear mixed in general as linear mixed models. Mixed-effects models is a more general term than the latter two. Mixed effects models—whether linear or generalized linear—are different in that there is more than one source of random variability in the data. Z is an n -by- q random-effects design matrix. Model 2 – Pizza consumption and timepoints included as predictors of mood. H��W˒�6��W�H�$����m���b;e+���DB+�\@E������[�d]�Ճ����4_�^����J�L�#����G����z�����y���?eF��*-d���-!�I��g��o��O�_@F�{��$O�9Y�� ��AT�E�2�V$���rE�y��ȒGA>X{��H�|�?XM�n���� k�(��X�K8�"g�.��H��Y�ey��M��#�gi9�;�5���eT&��|Ƴ��������-��a�l����Gbj�еx#E�D�~&y�C��P:�T�������P���j�q"l��H*�Y�z/�V�}�q)Ώ�L��nW�7�ӧ-|)���E�yxX�����g��y�kiC~�����ضes�[R��1r��NGq����c{钳�\�Xq��y�iq/�i`V�! If we divide the machine mean square by the mean square of the interaction effect we get 20.58. 0000048443 00000 n – Studies that obtain multiple measurements over time (longitudinal, time-series) or multiple trials per participant (within subjects) lend themselves well to mixed model analyses. Random effects are random variables in the population Typically assume that random effects are zero-mean Gaussian Typically want to estimate the variance parameter(s) Models with fixed and random effects are calledmixed-effects models. Thus, if you hold everything constant, the change in probability of the outcome over different values of your predictor of interest are only true when all covariates are held constant and you are in the same group, or a group with the same random effect. Ordered outcomes have been studied by, for The procedure uses the standard mixed model calculation engine to … Hence, the p-value of machine is given by. Linear Mixed Effects Models¶ Linear Mixed Effects models are used for regression analyses involving dependent data. The data set denotes: 1. students as s 2. instructors as d 3. departments as dept 4. service as service So, in interaction design and HCI studies, subject is a classic random effect. The null model will be fit to the maximal likelihood estimate. Logistic Mixed Effects Model with Interaction Term. For example, for unbalanced design with blocking, probably these methods … Mixed Effects Model can be used to model both linear and nonlinear relationships between dependent and independent variables. Mixed-effect linear models Whereas the classic linear model with n observational units and p predictors has the vectorized form with the predictor matrix , the vector of p + 1 coefficient estimates and the n -long vectors of the response and the residuals , LMMs additionally accomodate separate variance components modelled with a set of random effects , A mixed model is similar in many ways to a linear model. Now consider a standard regression model, i.e. I’ll be taking for granted some of the set-up steps from Lesson 1, so if you haven’t done that yet be sure to go back and do it. m2 <-glmer (outcome ~ var_binom * var_cont + (1 | group), data = dat, family = binomial (link = "logit")) To compute or plot marginal effects of interaction terms, simply specify these terms, i.e. In addition to students, there may be random variability from the teachers of those students. For example, we may assume there issome true regression line in the population, ββ,and we get some estimate of it, ^ββ^. Generally this is a higher-level variable that subjects or items are grouped under. %%EOF In this way, they provide a compromise between ignoring data groups entirely and fitting each group with a separate model. Each participant provided an average number of pizzas consumed, and measurements are collected at 15 timepoints. 0000007707 00000 n Mixed models are especially useful when working with a within-subjects design because it works around the ANOVA assumption that data points are independent of one another. A mixed model is similar in many ways to a linear model. if intercept increases, slope increases). Some terms might be more historical, others are more often seen in a specific discipline, others might refer to a certain data structure, and still others are special cases. If you are willing to assume that all the children have the same slope and intercept relating age to height then you can fit a regular linear … For example, an outcome may be measured more than once on the same person (repeated measures taken over time). A linear mixed effects model is a simple approach for modeling structured linear relationships (Harville, 1997; Laird and Ware, 1982). A revolution is taking place in the statistical analysis of psychological studies. If some models are livestock and some are pets, this model is my dearest pet. The effects are conditional on other predictors and group membership, which … To better understand slopes and intercepts it maybe helpful to imagine plotting the relationship between the IVs and DV for each subject. When to Use? Thus, we have a crossed design. In summary, we have seen how two schools of thought treat fixed and random effects, discussed when to use fixed effects and when to use random effects in both frameworks, discussed the assumptions behind the models, and seen how to implement a mixed effect model in R. Fixed and random effect models still remain a bit mysterious, but I hope that this discussion cleared up a few … Mixed-Effects … In a mixed-effects model, random effects contribute only to the covariance structure of the data. The ANOVA function allows you to compute Chi-squares between each model to see the improvement in model fit. Crossed designs occur when multiple measurements are associated with multiple grouping variables. The Mixed Modeling framework can specify a variety of model types including random coefficients models, hierarchical linear models, variance components models, nested models, and split-plot designs. 0000001225 00000 n To illustrate the use of mixed model approaches for analyzing repeated measures, we’ll examine a data set from Landau and Everitt’s 2004 book, “A Handbook of Statistical Analyses using SPSS”. This is Part 1 of a two part lesson. Pizza Study: Different baseline levels of pizza consumption across subjects, Pizza study: The strength of the relationship between pizza consumption and mood will vary from person to person, resulting in random slopes per subject. However, the researcher wants to be able to model how the alfalfas will grow in fields that are not in the experiment. The following example will illustrate the logic behind mixed effects models. The functions resid, coef, fitted, fixed.effects, and random.effects can be used to extract some of its components. Mixed effects models. If an effect, such as a medical treatment, affects the population mean, it is fixed. 0000000016 00000 n Some specific linear mixed effects models are. w�00�ng ���� ��A� �� p1 For example, in the above example we would most likely treat the mean income in a given ZIP as a sample from a normal distribution, with unknown mean and sigma to be estimated by the mixed … 0000000986 00000 n Mixed-effects models account for both fixed and random effects. Now consider a standard regression model, i.e. Mixed effects models are hierarchical in that they posit distributions for latent, unobserved parameters, but they are typically not fully Bayesian because the top-level hyperparameters will not be given proper priors. Note: due to the difference in scale of how the herbivore … As such, model 2 appears to be the best fit. For example, assume we have a dataset where again we are trying to model yield as a function of nitrogen level. Fixed effects are, essentially, your predictor variables. When building your models, you can treat your predictor as a fixed & random factor. 0000002636 00000 n Random effects are random variables in the population Typically assume that random effects are zero-mean Gaussian Typically want to estimate the variance parameter(s) Models with fixed and random effects are calledmixed-effects models. For example, a … ")����46�[l6�����t cj��"�ݑ�,�-�{9Z���NB��A���}[1���0��W�qG�x��+Ƴq9Q���Jx�J� ��7 #�ֱ)�S���Z ��h�H^F��e��lN��PK��"��ʓʎ�{���qC=��TgGEM*ٶ�1��Q��D�乕�үiGS��qe>™���WwL�K&���ʀ4��J6 3M�`��Y���p?�h^���8�G��0�m��yF�P�0�c�F����G�/�$TZn,]0E�/�EfRL�. For example, we may assume there is some true regression line in the population, \(\beta\), and we get some estimate of it, \(\hat{\beta}\). Definition. Mixed-effects models, however, recognize correlations within sample subgroups. Below are references for additional information # References Checking assumptions More theory here, here, and here. They are also common in scientific experiments where a given effect is assumed to be present among all study individuals which needs to be teased out from a … Slope: The strength of the relationship between IV & DV (controlling for randomness), which represent random effects. Random-effects terms are associated with individual experimental units drawn at random from a population, and account for variations between groups that might affect the response. Thus, the researcher makes the field where the alfalfa grows a random factor. Linear Mixed Effects models are used for regression analyses involving dependent data. The Mixed Modeling framework can specify a variety of model types including random coefficients models, hierarchical linear models, variance components models, nested models, and split-plot designs. This function can work with unbalanced designs: This function can work with unbalanced designs: lme1 = lme(yield ~ nf + bv * topo, random= ~1|rep, data=dat) We demonstrate with an example in Edward. Generalized linear mixed-effects models allow you to model more kinds of data, including binary responses and count data. … Because the purpose of this workshop is to show the use of the mixed command, rather than to teach about multilevel models in general, many topics important to multilevel modeling will be mentioned but not discussed in … Whereas before, analyses were limited to designs with a single random variable (either participants in so-called F1 analyses, or stimuli in so-called F2 analyses), mixed effects models currently allow researchers to take into account both participants and stimuli as random variables (Baayen, Davidson, & Bates, 2008; … The mixed-effects model that we would fit to these data, with random intercepts but no random slopes, is known as a random intercepts model. That is why mixed-effects is the terminology preferred here. SD reflects the amount of variation. Mixed Effects Logistic Regression Example. Mixed Effects Model can be used to model both linear and nonlinear relationships between dependent and independent variables. A mixed model is a good choice here: it will allow us to use all the data we have (higher sample size) and account for the correlations between data coming from the sites and mountain ranges. Linear Mixed-Effects Models y is the n -by-1 response vector, and n is the number of observations. Modeling conventions differ by field, but this example will begin by fitting the null model first, then building up hierarchically. If an effect is associated with a sampling procedure (e.g., subject effect), it is random. Another common set of experiments where linear mixed-effects models are used is repeated measures where time provide an additional source of correlation between measures. When to choose mixed-effects models, how to determine fixed effects vs. random effects, and nested vs. crossed sampling designs. Therefore, using a mixed model allows you to systematically account for item-level variability (within subjects) and subject-level variability (within groups). In a within subjects design, one participant provides multiple data points and those data will correlate with one another because they come from the same participant. NOTE - Predictor variables can be both fixed (i.e. In a within subjects design, one participant provides multiple data points and those data will correlate with one … We use the InstEval data set from the popular lme4 R package (Bates, Mächler, Bolker, & Walker, 2015). Mixed models are especially useful when working with a within-subjects design because it works around the ANOVA assumption that data points are independent of one another. This class of models are used to account for more than one source of random variation. 0000001774 00000 n Refer to the p-values in the output to see whether there was an improvement in fit. Random intercepts: Variability in baseline measurements, Fixed intercepts: Baseline variance is not affected. If an effect is associated with a Data. Is a mixed model right for your needs? This is exctly the value as in the output of the mixed model from above … To cover some frequently asked questions by users, we’ll fit a mixed model, inlcuding an interaction term and a quadratic resp. Random effects are best defined as noise in your data. trailer A random effect model is a model all of whose factors represent random effects. 0000000596 00000 n 0000002369 00000 n Mixed-effect models are common i n political polling analysis where national-level characteristics are assumed to occur at a state-level while state-level sample sizes may be too small to drive those characteristics on their own. It estimates the effects of one or more explanatory variables on a response variable. x�b```�],�@��Y8VpD�y�f� ��O�R���3Ϩ��0�K��3��6�USA�8�J5::@tZG�Ϥ$X"�E&Q ���`e�3LL�E@��kZ�����e�-�Ð�����p��.C:�s�;�� Mixed effects models A mixed model is a good choice here: it will allow us to use all the data we have (higher sample size) and account for the correlations between data coming from the … Code. The function does not do any scaling internally: the … Nonlinear mixed-effects models are applied in many fields including medicine, public health, pharmacology, and ecology. In addition to patients, there may also be random variability across the doctors of those patients. It is a data set of instructor evaluation ratings, where the inputs (covariates) include categories such as students and departments, and our response variable of interest is the instructor evaluation rating. A further mixed-effects model is applied to the three WER components SUB, DEL and INS to evaluate how they affect the two systems. See nlmeObject for the components of the fit. However, in mixed effects logistic models, the random effects also bear on the results. You should expect to see differences in the slopes of your random factors. %PDF-1.4 %���� 3.3 Types of mixed-effects models. Be able to make figures to … By the end of this lesson you will: Have learned the math of an LMEM. A revolution is taking place in the statistical analysis of psychological studies. Model 1 - Pizza consumption predict mood (main effect): This model appears to show pizza consumption as a positive predictor of mood, as indicated by a posi. Since we have … Value. <<050702A324ECEC43A1F0A889E3B500B8>]>> My analysis used a Bayesian nonlinear mixed effects beta regression model. However, this time the data were collected in many different farms. A model that contains both fixed and random effects is called a mixed model. Mixed-effects models, however, recognize correlations within sample subgroups. 63 0 obj <>stream The following equations represent a two-level model with one L1 predictor, X , and one L2 predictor, W . Note. endstream endobj 50 0 obj <> endobj 51 0 obj <>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>>/Type/Page>> endobj 52 0 obj <> endobj 53 0 obj <> endobj 54 0 obj <> endobj 55 0 obj [/ICCBased 60 0 R] endobj 56 0 obj <> endobj 57 0 obj <> endobj 58 0 obj <> endobj 59 0 obj <>stream The list of random effects implemented in INLA is quite rich. Effects coding Simulating data, ---
title: "Chapter 17: Mixed Effects Modeling"
author: "Sushmita Shrikanth"
output:
  html_document:
    theme: cerulean
    highlight: textmate
    fontsize: 8pt
    toc: true
    number_sections: true
    code_download: true
    toc_float:
      collapsed: false

---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE)
```

# Background Information
Mixed models are especially useful when working with a within-subjects design because it works around the ANOVA assumption that data points are independent of  one another. In a within subjects design, one participant provides multiple data points and those data will correlate with one another because they come from the same participant. Therefore, using a mixed model allows you to systematically account for item-level variability (within subjects) and subject-level variability (within groups).

**When to Use?** -- Studies that obtain multiple measurements over time (longitudinal, time-series) or multiple trials per participant (within subjects) lend themselves well to mixed model analyses.

The following example will illustrate the logic behind mixed effects models.

## Example: National Pizza Study
Let's say that we are interested in examining the effect of pizza consumption on people's moods. Each participant provided an average number of pizzas consumed, and measurements are collected at 15 timepoints 

- Hypothetical sample size, **n = 30**
- **DV**: Mood rating (scale)
- **IV1**: Pizza consumption 
- **IV2**: Time points (Weeks, 1-10)

Here is some hypothetical data (code used to generate data can be found [here](https://github.com/RInterested/SIMULATIONS_and_PROOFS/blob/master/Athletes%20mixed%20effects)): 

```{r include = FALSE}

rm(list = ls())
set.seed(0)
library(lme4)
library(mvtnorm)

subjects = 30
time = 10
 
i = 0.2 
s = 0.5 
r = 0.5
cov.matrix1<-  matrix(c(i^2, r * i * s, r * i * s, s^2), nrow = 2, byrow = T)

require(mvtnorm)
random.effects_subjects <-  rmvnorm(subjects, mean = c(0, 0), sigma = cov.matrix1)
subjects.df = data.frame(subject  = c(1:subjects)) 
subjects.df$alpha_subjects = 1 + random.effects_subjects[, 1]
subjects.df$beta_subjects =  2 + random.effects_subjects[, 2]

i =   0.8   
s =   0.2 
r = -0.01   
(cov.matrix2 <-  matrix(c(i^2, r * i * s, r * i * s, s^2), nrow = 2, byrow = T))

random.effects_time <-  rmvnorm(time, mean = c(0, 0), sigma = cov.matrix2)

time.df = data.frame(time  = c(1:time)) 
time.df$alpha_time   =    -1 + random.effects_time[, 1]
time.df$beta_time    =     1 + random.effects_time[, 2]
summary(time.df$beta_time) 
sd(time.df$beta_time)     
summary(time.df$alpha_time)
sd(time.df$alpha_time)
cor(time.df$alpha_time, time.df$beta_time) 

observations <- subjects * time
observations.df <-  data.frame(
  subject = sort(rep(c(1:subjects), time)),
  time = rep(c(1:time), subjects), 
  pizza = rep(rnorm(subjects * time, 30, 5)))
dat1   <-  merge(subjects.df, observations.df)
dat2   <-  merge(dat1, time.df)
dat3   <-  dat2[with(dat2, order(subject,time)), ]
rownames(dat3)   <-  1:nrow(dat3)


df <-  within(dat3, 
              mood <-  alpha_subjects + pizza * beta_subjects +
                alpha_time    + pizza * beta_time    +
                0.75 * rnorm(n = observations)) 

head(df)
pizzadata <- df[,-c(3,4,6,7)]
```


```{r echo = FALSE}
head(pizzadata)

```

**NOTE** - This is a within-subjects study. All participants are providing multiple measurements. 

## Important Terminology 
Below are some important terms to know for understanding the statistical concepts used in mixed models:

###Crossed & Nested Designs
**Crossed designs** refer to the *within-subject* variables (i.e. timepoint, condition, etc.). Crossed designs occur when multiple measurements are associated with multiple grouping variables. In a completely crossed design, all subjects provide responses for all conditions/time-points.

  - Pizza study: We have subjects providing responses at 10 time points. Thus, we have a crossed design. 
  
**Nested designs** refer to the *between-subject* variable. Generally this is a higher-level variable that subjects or items are grouped under.
  
  - Pizza study: Not nested.

###Fixed v. Random Effects
**Fixed effects** are, essentially, your predictor variables. This is the effect you are interested in after accounting for random variability (hence, fixed). 
 
  - Pizza study: The fixed effects are PIZZA consumption and TIME, because we're interested in the effect of pizza consumption on MOOD, and if this effect varies over TIME. 
  
**Random effects** are best defined as noise in your data. These are effects that arise from uncontrollable variability within the sample. *Subject* level variability is often a random effect.
 
  - Pizza study: Controlling for random effects of subject, pizza consumption, and effect of time on subject, all of which vary across participants. 

**NOTE** - Predictor variables can be both fixed (i.e. causing a main effect/interaction) and random (i.e. causing variance/variability in responses). When building your models, you can treat your predictor as a fixed & random factor. 

### Slopes v. Intercepts: 
To better understand slopes and intercepts it maybe helpful to imagine plotting the relationship between the IVs and DV for each subject.

**Intercepts**: The baseline relationship between IV & DV. Fixed effects are plotted as intercepts to reflect the baseline level of your DV.
  
  -	Random intercepts: Variability in baseline measurements 
      
      * Pizza Study: Different baseline levels of pizza consumption across subjects
      
  - Fixed intercepts: Baseline variance is not affected
  
      * Pizza study: 

**Slope**: The strength of the relationship between IV & DV (controlling for randomness), which represent random effects. You should expect to see differences in the slopes of your random factors. 
  
  - Pizza study: The strength of the relationship between pizza consumption and mood will vary from person to person, resulting in random slopes per subject. Because subjects start at  

**Note**: If 2 variables share a lot of variance, the random intercepts and slopes may be correlated with one another. This can be accounted for in random structures as well. 

**Hypotheses For Study**
Random effects: 
- "Subjects" will have their own intercepts. 
- Subjects' slope will vary by pizza consumption intercepts, and by timepoint intercepts. 
- The slopes and intercepts of pizza consumption and time will be correlated (shared variance)
Fixed effects: 
- Expecting there to be an overall main effect of pizza consumption over time. 
- Expecting interaction such that more pizza over time predicts mood. 

# Setting up data in R 
- **Coding**: Recode your variable (mean-centered, effects) as best suited for your data. 
- **Long Format** : Refer to [TidyR chapter](http://ademos.people.uic.edu/Chapter9.html) 
- **Packages**: Make sure you have the following packages downloaded: 

``` {r, message=FALSE, echo=TRUE}

library (lmerTest) # Mixed model package by Douglas Bates, comes w/ pvalues! 
library (texreg) #Helps us make tables of the mixed models
library (afex) # Easy ANOVA package to compare model fits
library (plyr) # Data manipulator package
library (ggplot2) # GGplot package for visualizing data

```


#Modeling Procedure
Modeling conventions differ by field, but this example will begin by fitting the null model first, then building up hierarchically.
 

## Random effects structure
The *null model* will be fit to the [maximal likelihood estimate](http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf). The random effects structure reflects YOUR understanding of where to expect variance, and how nested data will interact with that variance. The general syntax is as follows:

``` 
(1 + IV | unit level)  
(1 + IV.1*IV.2 | unit level)

#or

(0 + IV | unit level)
(0 + IV.1*IV.2 | unit level)

```
When there is a 1 before the line, you are accounting for random intercepts (varying baseline levels) in your variable. A O indicates the variable has a fixed intercept and not a random one.  These are a few hypothetical random effects structures:

  - ```(1| subject)``` = Random intercepts and slopes for subjects (different baselines, different average effect per subject).
  - ```(1 + pizza |subject)``` = The effect of pizza will vary *between* subjects. Random intercepts for pizza consumption, random slopes
for subjects influenced by pizza consumption. 
  - ``` (1 + pizza | subject) + (0 + time| subject)``` = Subjects have random intercepts and slopes as influenced by pizza consumption. Time slopes can vary as function of the subject, but variance between pizza consumption and time as independent
  - ``` (1 + pizza + time | subject)``` = Same as above, but variance between pizza consumption and time are SHARED (pizza consumption has relationship with time that varies by subject). 
  - ``` (1 + pizza * time | subject)`` =  Each subject can have their intercept, random slopes influenced by pizza and time, and their interaction between pizza and time. IMPORTANTLY, all random slopes and intercepts can be *correlated*. 
  
### Fitting Best Random Effects Structure
The ```lmer``` package can be used for modeling, and the general syntax is as follows: 
 ```
 modelname <- lmer (dv ~ 1 + IV +(randomeffects), data = data.name, REML = FALSE)
 
 ```

You can name each model whatever you want, but note that the name of the dataframe containing your data is specified in each model. Keep ``` REML = FALSE ```. 

First, however, we need to specify the random effects term that best fits the data. Try out different structures, and use the ```anova``` function to find the best fitting random effects structure. This function compares the fit of the model to see how fit has improved with additional items. You can also **visualize your data** to see what fits. ### Insert ggplot2 reference.  

``` {r echo = TRUE, message = FALSE}
nullmodel1 <- lmer( mood ~ 1 + (1|subject), data = pizzadata, REML=FALSE)
nullmodel2 <- lmer( mood ~ 1 + (1 + pizza |subject), data = pizzadata, REML=FALSE)
nullmodel3 <- lmer( mood ~ 1 + (1 + pizza * time |subject), data = pizzadata, REML=FALSE)

anova (nullmodel1, nullmodel2, nullmodel3)
```

Refer to the p-values in the output to see whether there was an improvement in fit. Because there was an improvement in between model 1 and model 2, but NO improvement between model 2 and model 3, we can proceed using the best fit model, `nullmodel2`, as our random effects structure for the rest of the analyses. 

## Fixed effects
Specific predictors can now be introduced into our model by specifying the DV followed by the predictor, random effects, and the dataframe. 

**Model 1** - Pizza consumption predict mood (main effect): 

```{r echo = TRUE, message = FALSE, error = FALSE}
m1=lmer(mood ~ pizza + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m1)

```

This model appears to show pizza consumption as a positive predictor of mood, as indicated by a posi

Random effects: 

  - SD reflects the amount of variation. Check correlation between intercept and slope (i.e. if intercept increases, slope increases). 
    
Fixed effects

  - Check estimates for beta value -- time has a significant effect, improvement in mood by about 1 point over time. 
  - Check correlation of fixed effects -- if too high, this may imply [multicollinearity](http://ademos.people.uic.edu/Chapter13.html)

**Model 2** -- Pizza consumption and timepoints included as predictors of mood. 
```{r echo = TRUE, message = FALSE, error = FALSE}
m2= lmer(mood ~ pizza + time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m2)

```

```{r echo = TRUE, message = FALSE, error = FALSE}
m2= lmer(mood ~ pizza + time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m2)

```

Results show significant effects of both pizza consumption and time on mood! Do they interact? 

**Model 3** -- Including an interaction term between pizza consumption and time (pizza consumption varies over time)

```{r echo = TRUE, message = FALSE, error = FALSE}
m3 = lmer(mood ~ pizza*time + (1 + pizza + time |subject), data=pizzadata, REML = FALSE)
summary(m3)

```

Results show that while pizza consumption and time are still significant main predictors, their interaction term did not reach significance. 

## Comparing Model Fit 
The ANOVA function allows you to compute Chi-squares between each model to see the improvement in model fit. The `effects` package should also include p-values in the output. 

```{r echo = TRUE}

anova (m1, m2, m3)

```

As you can see by the p-values, while there is an improvement in fit from model 1 to model 2, model 3 did not explain more variance. As such, model 2 appears to be the best fit.

We can now conclude that after controlling for random effects, more pizza consumption does lead to improvements in mood over time, but there is no interaction with time. 

This concludes the tutorial on mixed effects models. Below are references for additional information 
# References 
[Checking assumptions](http://ademos.people.uic.edu/Chapter18.html)
[More theory here](http://www.stat.cmu.edu/~hseltman/309/Book/chapter15.pdf), [here](http://jakewestfall.org/misc/BDB2008.pdf), and [here](http://www.bodowinter.com/tutorial/bw_LME_tutorial2.pdf).
[Effects coding](http://www.martijnwieling.nl/R/sheets.pdf)
[Simulating data](http://anythingbutrbitrary.blogspot.in/2012/10/hierarchical-linear-models-and-lmer.html)

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