prepro and models vignette edits

* fix bolixed math
* pivot simply
* deal with training = NULL in `prep()`

vignettes/preprocessing-and-models.Rmd

@@ -98,10 +98,11 @@ intercept coefficients, we can allow for an intercept shift between states.
 
 The model takes the form
 \begin{aligned}
-\log\left( \mu*{t+7} \right) &= \beta_0 + \delta_1 s*{\text{state}_1} +
-\delta_2 s_{\text{state}_2} + \cdots + \nonumber \\ &\quad\beta_1 \text{deaths}_{t} +
-\beta*2 \text{deaths}*{t-7} + \beta*3 \text{cases}*{t} +
-\beta*4 \text{cases}*{t-7},
+\log\left( \mu_{t+7} \right) &= \beta_0 + \delta_1 s_{\text{state}_1} +
+\delta_2 s_{\text{state}_2} + \cdots + \nonumber \\ 
+&\quad\beta_1 \text{deaths}_{t} +
+\beta_2 \text{deaths}_{t-7} + \beta_3 \text{cases}_{t} +
+\beta_4 \text{cases}_{t-7},
 \end{aligned}
 where $\mu_{t+7} = \mathbb{E}(y_{t+7})$, and $y_{t+7}$ is assumed to follow a
 Poisson distribution with mean $\mu_{t+7}$; $s_{\text{state}}$ are dummy
@@ -195,11 +196,13 @@ rates, by incorporating offset terms in the model.
 
 To model death rates, the Poisson regression would be expressed as:
 \begin{aligned}
-\log\left( \mu*{t+7} \right) &= \log(\text{population}) +
-\beta_0 + \delta_1 s*{\text{state}_1} +
-\delta_2 s_{\text{state}_2} + \cdots + \nonumber \\ &\quad\beta_1 \text{deaths}_{t} +
-\beta*2 \text{deaths}*{t-7} + \beta*3 \text{cases}*{t} +
-\beta*4 \text{cases}*{t-7}\end{aligned}
+\log\left( \mu_{t+7} \right) &= \log(\text{population}) +
+\beta_0 + \delta_1 s_{\text{state}_1} +
+\delta_2 s_{\text{state}_2} + \cdots + \nonumber \\ 
+&\quad\beta_1 \text{deaths}_{t} +
+\beta_2 \text{deaths}_{t-7} + \beta_3 \text{cases}_{t} +
+\beta_4 \text{cases}_{t-7}
+\end{aligned}
 where $\log(\text{population})$ is the log of the state population that was
 used to scale the count data on the left-hand side of the equation. This offset
 is simply a predictor with coefficient fixed at 1 rather than estimated.
@@ -371,9 +374,7 @@ To look at the prediction intervals:
 ```{r}
 p %>%
   select(geo_value, target_date, .pred_scaled, .pred_distn_scaled) %>%
-  mutate(.pred_distn_scaled = nested_quantiles(.pred_distn_scaled)) %>%
-  unnest(.pred_distn_scaled) %>%
-  pivot_wider(names_from = quantile_levels, values_from = values)
+  pivot_quantiles_wider(.pred_distn_scaled)
 ```
 
 Last but not least, let's take a look at the regression fit and check the
@@ -425,16 +426,16 @@ $$
 where $j$ is either down, flat, or up
 
 \begin{aligned}
-g*{\text{down}}(x) &= 0.\\
-g*{\text{flat}}(x)&= \text{ln}\left(\frac{Pr(Z*{\ell,t}=\text{flat}|x)}{Pr(Z*{\ell,t}=\text{down}|x)}\right) =
-\beta*{10} + \beta*{11}t + \delta*{10} s*{\text{state*1}} +
-\delta*{11} s*{\text{state_2}} + \cdots \nonumber \\
-&\quad + \beta*{12} Y^{\Delta}_{\ell, t} +
+g_{\text{down}}(x) &= 0.\\
+g_{\text{flat}}(x) &= \log\left(\frac{Pr(Z_{\ell,t}=\text{flat}\mid x)}{Pr(Z_{\ell,t}=\text{down}\mid x)}\right) =
+\beta_{10} + \beta_{11} t + \delta_{10} s_{\text{state_1}} +
+\delta_{11} s_{\text{state_2}} + \cdots \nonumber \\
+&\quad + \beta_{12} Y^{\Delta}_{\ell, t} +
 \beta_{13} Y^{\Delta}_{\ell, t-7} \\
-g_{\text{flat}}(x) &= \text{ln}\left(\frac{Pr(Z*{\ell,t}=\text{up}|x)}{Pr(Z*{\ell,t}=\text{down}|x)}\right) =
-\beta*{20} + \beta*{21}t + \delta*{20} s*{\text{state*1}} +
-\delta*{21} s*{\text{state}\_2} + \cdots \nonumber \\
-&\quad + \beta*{22} Y^{\Delta}_{\ell, t} +
+g_{\text{flat}}(x) &= \log\left(\frac{Pr(Z_{\ell,t}=\text{up}\mid x)}{Pr(Z_{\ell,t}=\text{down} \mid x)}\right) =
+\beta_{20} + \beta_{21}t + \delta_{20} s_{\text{state_1}} +
+\delta_{21} s_{\text{state}\_2} + \cdots \nonumber \\
+&\quad + \beta_{22} Y^{\Delta}_{\ell, t} +
 \beta_{23} Y^{\Delta}\_{\ell, t-7}
 \end{aligned}
 
@@ -533,7 +534,7 @@ p1 <- epi_recipe(ex) %>%
   step_epi_lag(death_rate, lag = c(0, 7, 14)) %>%
   step_epi_ahead(death_rate, ahead = 7, role = "outcome") %>%
   step_epi_naomit() %>%
-  prep()
+  prep(ex)
 
 b1 <- bake(p1, ex)
 b1
@@ -550,7 +551,7 @@ p2 <- epi_recipe(ex) %>%
     ahead7death_rate = lead(death_rate, 7)
   ) %>%
   step_epi_naomit() %>%
-  prep()
+  prep(ex)
 
 b2 <- bake(p2, ex)
 b2