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https://github.com/tjmahr/huttenlocher1991

Vocabulary growth in 22 infants (Huttenlocher et al., 1991)
https://github.com/tjmahr/huttenlocher1991

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Vocabulary growth in 22 infants (Huttenlocher et al., 1991)

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README 

        
---

output: github_document

---



```{r, include = FALSE}

knitr::opts_chunk$set(

  collapse = TRUE,

  comment = "#>",

  fig.path = "man/figures/README-",

  out.width = "100%"

)

library(tidyverse)

```



# huttenlocher1991



This package provides the vocabulary growth data from the following article:



> Huttenlocher, J., Haight, W., Bryk, A., Seltzer, M., & Lyons, T. (1991). Early

> vocabulary growth: Relation to language input and gender. *Developmental

> Psychology*, *27*(2), 236–248. 



This dataset is useful educationally because it features longitudinal/repeated

measures growth data. It is also unusual because in the associated article, the

only fixed effect predictor for growth is quadratic time--that is, there are

no intercept or linear time terms.



I retrieved this data from the [HLM software's examples

page](https://ssicentral.com/index.php/products/hlm-general/hlm-examples/) and

created a .csv-file out of it.



## Installation



You can install the development version of huttenlocher1991 like so:



``` r

remotes::install_github("tjmahr/huttenlocher1991")

```



## Example



Here are the data all plotted.



```{r}

#| spag-1, fig.width = 3, fig.height = 2.5, dpi = 300, out.width = "50%"

library(huttenlocher1991)

library(tidyverse)



vocab_growth



ggplot(vocab_growth) + 

  aes(x = age, y = vocab) + 

  geom_line(aes(group = id))

```



Here is the "obvious" fully specified growth model.



```{r}

library(lme4)



m <- lmer(

  vocab ~ age_12 + age_12_sq + (age_12 + age_12_sq | id),

  vocab_growth

)

summary(m)

```



They note in footnote 2 that there was high collinearity between

π1*i* and π2*i* (the two random slopes) which we see

above.



They use a reduced quadratic model, which I think was basically:



```{r}

mr <- lmer(

  vocab ~  0 + age_12_sq + (0 + age_12_sq | id),

  vocab_growth

)

summary(mr)

```



There is no intercept because at x = 0 (age = 12 months), vocabulary should be 0 (?).



If I include `group`, I can reproduce the coefficients from Table 1, which makes

me think I am on the right track.



```{r}

mr_group <- lmer(

  vocab ~  0 + age_12_sq + age_12_sq:group + (0 + age_12_sq | id),

  vocab_growth

)

summary(mr_group)

```



Finally, we can recreate the figures:



```{r}

#| spag-2, fig.width = 3, fig.height = 2.5, dpi = 300, out.width = "50%"

library(broom.mixed)

data <- mr %>% 

  augment(newdata = vocab_growth)



ggplot(data %>% filter(id %in% c(11, 5, 7))) +

  aes(x = age, y = vocab, shape = factor(id)) +

  geom_point() +

  geom_line(aes(y = .fitted, linetype = factor(id))) + 

  guides(shape = "none", linetype = "none") + 

  labs(x = "age [months]", y = "vocabulary")



knitr::include_graphics("man/figures/f1.png")

```



Excluding the intercept entirely reminded me of nonlinear models, so can we just

one of those?



```{r}

nform <- ~ beta * input ^ 2

nfun <- deriv(

  nform, 

  namevec = "beta", 

  function.arg = c("input", "beta")

)



mr_nl <- nlmer(

  vocab ~ nfun(age_12, beta) ~ beta | id, 

  data = vocab_growth, 

  start = c(beta = 0)

)



summary(mr_nl)



fixef(mr_nl)

fixef(mr)



VarCorr(mr_nl)

VarCorr(mr)

```