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updates lmer
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64 changes: 15 additions & 49 deletions 19-linear_mixed_effects_models3.Rmd
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- Pitfalls in fitting `lmers()`s (and what to do about it).
- Understanding `lmer()` syntax even better.
- ANOVA vs. Lmer
- ANOVA vs. lmer

## Load packages and set plotting theme

Expand Down Expand Up @@ -42,53 +42,12 @@ options(dplyr.summarise.inform = F)

## Load data sets

### Sleep data

```{r}
# load sleepstudy data set
df.sleep = sleepstudy %>%
as_tibble() %>%
clean_names() %>%
mutate(subject = as.character(subject)) %>%
select(subject, days, reaction)
# add two fake participants (with missing data)
df.sleep = df.sleep %>%
bind_rows(tibble(subject = "374",
days = 0:1,
reaction = c(286, 288)),
tibble(subject = "373",
days = 0,
reaction = 245))
```

### Reasoning data

```{r}
df.reasoning = sk2011.1
```

### Weight loss data

```{r}
data("weightloss", package = "datarium")
# Modify it to have three-way mixed design
df.weightloss = weightloss %>%
mutate(id = rep(1:24, 2)) %>%
pivot_longer(cols = t1:t3,
names_to = "timepoint",
values_to = "score") %>%
arrange(id)
```

### Politness data

```{r}
df.politeness = read_csv("data/politeness_data.csv") %>%
mutate(scenario = as.factor(scenario))
```

## Understanding the lmer() syntax

Here is an overview of how to specify different kinds of linear mixed effects models.
Expand All @@ -99,7 +58,7 @@ tibble(formula = c("`dv ~ x1 + (1 | g)`",
"`dv ~ x1 + (x1 | g)`",
"`dv ~ x1 + (x1 || g)`",
"`dv ~ x1 + (1 | school) + (1 | teacher)`",
"`dv ~ x1 + (1 | school/teacher)`"),
"`dv ~ x1 + (1 | school) + (1 | school:teacher)`"),
description = c("Random intercept for each level of `g`",
"Random slope for each level of `g`",
"Correlated random slope and intercept for each level of `g`",
Expand All @@ -111,7 +70,7 @@ tibble(formula = c("`dv ~ x1 + (1 | g)`",

Note that this `(1 | school/teacher)` is equivalent to `(1 | school) + (1 | teacher:school)` (see [here](https://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specified)).

## ANOVA vs. Lmer
## ANOVA vs. lmer

### Between subjects ANOVA

Expand All @@ -128,7 +87,7 @@ aov_ez(id = "id",

Looks like there was no main effect of `instruction` on participants' responses.

An alternative route for getting at the same test, would be via combining `lm()` with `Anova()` (as we've done before in class).
An alternative route for getting at the same test, would be via combining `lm()` with `joint_tests()` (as we've done before in class).

```{r}
lm(formula = response ~ instruction,
Expand All @@ -153,10 +112,11 @@ aov_ez(id = "id",
filter(instruction == "probabilistic"))
```

For the linear model route, given that we have repeated observations from the same participants, we need to use `lmer()`. The repeated measures anova has the random effect structure as shown below:
For the linear model route, given that we have repeated observations from the same participants, we need to use `lmer()`. The repeated measures ANOVA has the random effect structure as shown below:

```{r}
lmer(formula = response ~ validity * plausibility + (1 | id) + (1 | validity:id) + (1 | plausibility:id),
lmer(formula = response ~ 1 + validity * plausibility + (1 | id) +
(1 | id:validity) + (1 | id:plausibility),
data = df.reasoning %>%
filter(instruction == "probabilistic") %>%
group_by(id, validity, plausibility) %>%
Expand All @@ -183,15 +143,21 @@ aov_ez(id = "id",
with the `lmer()` route:

```{r}
lmer(formula = response ~ instruction * validity * plausibility + (1 | id) + (1 | validity:id) + (1 | plausibility:id),
lmer(formula = response ~ instruction * validity * plausibility + (1 | id) +
(1 | id:validity) + (1 | id:plausibility),
data = df.reasoning %>%
group_by(id, validity, plausibility, instruction) %>%
summarize(response = mean(response))) %>%
joint_tests()
```

Here, both routes yield the same results.

## Additional resources

### Readings

- [Nested and crossed random effects in lme4](https://www.muscardinus.be/statistics/nested.html)

## Session info

Information about this R session including which version of R was used, and what packages were loaded.
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10 changes: 7 additions & 3 deletions 20-linear_mixed_effects_models4.Rmd
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Expand Up @@ -228,11 +228,14 @@ ggplot(data = df.politeness,
We fit the model and compute the contrasts.

```{r, message=FALSE}
fit = lmer(formula = frequency ~ 1 + attitude * gender + (1 | subject) + (1 | scenario),
fit = lmer(formula = frequency ~ 1 + attitude * gender + (1 + attitude | subject) + (1 | scenario),
data = df.politeness)
fit %>%
emmeans(specs = pairwise ~ attitude + gender,
joint_tests()
fit %>%
emmeans(specs = pairwise ~ attitude + gender,
adjust = "none")
```

Expand Down Expand Up @@ -492,7 +495,8 @@ df.boot = df.sleep %>%
bootstrap(n = 100,
id = "id") %>%
mutate(fit = map(.x = strap,
.f = ~ lm(formula = reaction ~ 1 + days, data = .)),
.f = ~ lm(formula = reaction ~ 1 + days,
data = .x)),
tidy = map(.x = fit,
.f = tidy)) %>%
unnest(tidy) %>%
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31 changes: 16 additions & 15 deletions docs/404.html
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<meta name="author" content="Tobias Gerstenberg" />


<meta name="date" content="2024-02-22" />
<meta name="date" content="2024-02-25" />

<meta name="viewport" content="width=device-width, initial-scale=1" />
<meta name="apple-mobile-web-app-capable" content="yes" />
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<li class="chapter" data-level="19.2" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#load-packages-and-set-plotting-theme-12"><i class="fa fa-check"></i><b>19.2</b> Load packages and set plotting theme</a></li>
<li class="chapter" data-level="19.3" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#load-data-sets-4"><i class="fa fa-check"></i><b>19.3</b> Load data sets</a>
<ul>
<li class="chapter" data-level="19.3.1" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#sleep-data"><i class="fa fa-check"></i><b>19.3.1</b> Sleep data</a></li>
<li class="chapter" data-level="19.3.2" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#reasoning-data"><i class="fa fa-check"></i><b>19.3.2</b> Reasoning data</a></li>
<li class="chapter" data-level="19.3.3" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#weight-loss-data"><i class="fa fa-check"></i><b>19.3.3</b> Weight loss data</a></li>
<li class="chapter" data-level="19.3.4" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#politness-data"><i class="fa fa-check"></i><b>19.3.4</b> Politness data</a></li>
<li class="chapter" data-level="19.3.1" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#reasoning-data"><i class="fa fa-check"></i><b>19.3.1</b> Reasoning data</a></li>
</ul></li>
<li class="chapter" data-level="19.4" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#understanding-the-lmer-syntax"><i class="fa fa-check"></i><b>19.4</b> Understanding the lmer() syntax</a></li>
<li class="chapter" data-level="19.5" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#anova-vs.-lmer"><i class="fa fa-check"></i><b>19.5</b> ANOVA vs. Lmer</a>
<li class="chapter" data-level="19.5" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#anova-vs.-lmer"><i class="fa fa-check"></i><b>19.5</b> ANOVA vs. lmer</a>
<ul>
<li class="chapter" data-level="19.5.1" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#between-subjects-anova"><i class="fa fa-check"></i><b>19.5.1</b> Between subjects ANOVA</a></li>
<li class="chapter" data-level="19.5.2" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#repeated-measures-anova"><i class="fa fa-check"></i><b>19.5.2</b> Repeated-measures ANOVA</a></li>
<li class="chapter" data-level="19.5.3" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#mixed-anova"><i class="fa fa-check"></i><b>19.5.3</b> Mixed ANOVA</a></li>
</ul></li>
<li class="chapter" data-level="19.6" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#session-info-18"><i class="fa fa-check"></i><b>19.6</b> Session info</a></li>
<li class="chapter" data-level="19.6" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#additional-resources-17"><i class="fa fa-check"></i><b>19.6</b> Additional resources</a>
<ul>
<li class="chapter" data-level="19.6.1" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#readings-2"><i class="fa fa-check"></i><b>19.6.1</b> Readings</a></li>
</ul></li>
<li class="chapter" data-level="19.7" data-path="linear-mixed-effects-models-3.html"><a href="linear-mixed-effects-models-3.html#session-info-18"><i class="fa fa-check"></i><b>19.7</b> Session info</a></li>
</ul></li>
<li class="chapter" data-level="20" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html"><i class="fa fa-check"></i><b>20</b> Linear mixed effects models 4</a>
<ul>
<li class="chapter" data-level="20.1" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#learning-goals-11"><i class="fa fa-check"></i><b>20.1</b> Learning goals</a></li>
<li class="chapter" data-level="20.2" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#load-packages-and-set-plotting-theme-13"><i class="fa fa-check"></i><b>20.2</b> Load packages and set plotting theme</a></li>
<li class="chapter" data-level="20.3" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#load-data-sets-5"><i class="fa fa-check"></i><b>20.3</b> Load data sets</a>
<ul>
<li class="chapter" data-level="20.3.1" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#sleep-data-1"><i class="fa fa-check"></i><b>20.3.1</b> Sleep data</a></li>
<li class="chapter" data-level="20.3.1" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#sleep-data"><i class="fa fa-check"></i><b>20.3.1</b> Sleep data</a></li>
<li class="chapter" data-level="20.3.2" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#reasoning-data-1"><i class="fa fa-check"></i><b>20.3.2</b> Reasoning data</a></li>
<li class="chapter" data-level="20.3.3" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#weight-loss-data-1"><i class="fa fa-check"></i><b>20.3.3</b> Weight loss data</a></li>
<li class="chapter" data-level="20.3.4" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#politness-data-1"><i class="fa fa-check"></i><b>20.3.4</b> Politness data</a></li>
<li class="chapter" data-level="20.3.3" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#weight-loss-data"><i class="fa fa-check"></i><b>20.3.3</b> Weight loss data</a></li>
<li class="chapter" data-level="20.3.4" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#politness-data"><i class="fa fa-check"></i><b>20.3.4</b> Politness data</a></li>
</ul></li>
<li class="chapter" data-level="20.4" data-path="linear-mixed-effects-models-4.html"><a href="linear-mixed-effects-models-4.html#follow-up-tests-with-emmeans"><i class="fa fa-check"></i><b>20.4</b> Follow-up tests with emmeans</a>
<ul>
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<li class="chapter" data-level="22.4.2" data-path="bayesian-data-analysis-1.html"><a href="bayesian-data-analysis-1.html#frequentist-analysis"><i class="fa fa-check"></i><b>22.4.2</b> Frequentist analysis</a></li>
<li class="chapter" data-level="22.4.3" data-path="bayesian-data-analysis-1.html"><a href="bayesian-data-analysis-1.html#bayesian-regression"><i class="fa fa-check"></i><b>22.4.3</b> Bayesian regression</a></li>
</ul></li>
<li class="chapter" data-level="22.5" data-path="bayesian-data-analysis-1.html"><a href="bayesian-data-analysis-1.html#additional-resources-17"><i class="fa fa-check"></i><b>22.5</b> Additional resources</a>
<li class="chapter" data-level="22.5" data-path="bayesian-data-analysis-1.html"><a href="bayesian-data-analysis-1.html#additional-resources-18"><i class="fa fa-check"></i><b>22.5</b> Additional resources</a>
<ul>
<li class="chapter" data-level="22.5.1" data-path="bayesian-data-analysis-1.html"><a href="bayesian-data-analysis-1.html#books-and-chapters-5"><i class="fa fa-check"></i><b>22.5.1</b> Books and chapters</a></li>
</ul></li>
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<li class="chapter" data-level="23.7.2" data-path="bayesian-data-analysis-2.html"><a href="bayesian-data-analysis-2.html#specify-and-fit-the-model-3"><i class="fa fa-check"></i><b>23.7.2</b> 2. Specify and fit the model</a></li>
<li class="chapter" data-level="23.7.3" data-path="bayesian-data-analysis-2.html"><a href="bayesian-data-analysis-2.html#test-specific-hypotheses-3"><i class="fa fa-check"></i><b>23.7.3</b> 5. Test specific hypotheses</a></li>
</ul></li>
<li class="chapter" data-level="23.8" data-path="bayesian-data-analysis-2.html"><a href="bayesian-data-analysis-2.html#additional-resources-18"><i class="fa fa-check"></i><b>23.8</b> Additional resources</a></li>
<li class="chapter" data-level="23.8" data-path="bayesian-data-analysis-2.html"><a href="bayesian-data-analysis-2.html#additional-resources-19"><i class="fa fa-check"></i><b>23.8</b> Additional resources</a></li>
<li class="chapter" data-level="23.9" data-path="bayesian-data-analysis-2.html"><a href="bayesian-data-analysis-2.html#session-info-22"><i class="fa fa-check"></i><b>23.9</b> Session info</a></li>
</ul></li>
<li class="chapter" data-level="24" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html"><i class="fa fa-check"></i><b>24</b> Bayesian data analysis 3</a>
Expand All @@ -771,7 +772,7 @@
<li class="chapter" data-level="24.6.4" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html#gaussian-regression-unequal-variance"><i class="fa fa-check"></i><b>24.6.4</b> Gaussian regression (unequal variance)</a></li>
<li class="chapter" data-level="24.6.5" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html#model-comparison-2"><i class="fa fa-check"></i><b>24.6.5</b> Model comparison</a></li>
</ul></li>
<li class="chapter" data-level="24.7" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html#additional-resources-19"><i class="fa fa-check"></i><b>24.7</b> Additional resources</a></li>
<li class="chapter" data-level="24.7" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html#additional-resources-20"><i class="fa fa-check"></i><b>24.7</b> Additional resources</a></li>
<li class="chapter" data-level="24.8" data-path="bayesian-data-analysis-3.html"><a href="bayesian-data-analysis-3.html#session-info-23"><i class="fa fa-check"></i><b>24.8</b> Session info</a></li>
</ul></li>
<li class="chapter" data-level="25" data-path="model-assumptions.html"><a href="model-assumptions.html"><i class="fa fa-check"></i><b>25</b> Model assumptions</a>
Expand All @@ -786,7 +787,7 @@
<li class="chapter" data-level="25.3.4" data-path="model-assumptions.html"><a href="model-assumptions.html#non-parametric-tests"><i class="fa fa-check"></i><b>25.3.4</b> Non-parametric tests</a></li>
<li class="chapter" data-level="25.3.5" data-path="model-assumptions.html"><a href="model-assumptions.html#bootstrapping-regressions"><i class="fa fa-check"></i><b>25.3.5</b> Bootstrapping regressions</a></li>
</ul></li>
<li class="chapter" data-level="25.4" data-path="model-assumptions.html"><a href="model-assumptions.html#additional-resources-20"><i class="fa fa-check"></i><b>25.4</b> Additional resources</a></li>
<li class="chapter" data-level="25.4" data-path="model-assumptions.html"><a href="model-assumptions.html#additional-resources-21"><i class="fa fa-check"></i><b>25.4</b> Additional resources</a></li>
<li class="chapter" data-level="25.5" data-path="model-assumptions.html"><a href="model-assumptions.html#session-info-24"><i class="fa fa-check"></i><b>25.5</b> Session info</a></li>
</ul></li>
<li class="chapter" data-level="26" data-path="reporting-statistics.html"><a href="reporting-statistics.html"><i class="fa fa-check"></i><b>26</b> Reporting statistics</a>
Expand All @@ -803,7 +804,7 @@
<ul>
<li class="chapter" data-level="26.2.1" data-path="reporting-statistics.html"><a href="reporting-statistics.html#frequentist-statistics"><i class="fa fa-check"></i><b>26.2.1</b> Frequentist statistics</a></li>
</ul></li>
<li class="chapter" data-level="26.3" data-path="reporting-statistics.html"><a href="reporting-statistics.html#additional-resources-21"><i class="fa fa-check"></i><b>26.3</b> Additional resources</a>
<li class="chapter" data-level="26.3" data-path="reporting-statistics.html"><a href="reporting-statistics.html#additional-resources-22"><i class="fa fa-check"></i><b>26.3</b> Additional resources</a>
<ul>
<li class="chapter" data-level="26.3.1" data-path="reporting-statistics.html"><a href="reporting-statistics.html#misc-12"><i class="fa fa-check"></i><b>26.3.1</b> Misc</a></li>
</ul></li>
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