rerun vignettes

doc/brms_customfamilies.Rmd

@@ -42,6 +42,9 @@ list of distributions, which are not natively supported. The present vignette
 will explain how to specify such *custom families* in **brms**. By doing that,
 users can benefit from the modeling flexibility and post-processing options of
 **brms** even when using self-defined response distributions.
+If you have built a custom family that you want to make available to other
+users, you can submit a pull request to this 
+[GitHub repository](https://github.com/paul-buerkner/custom-brms-families).
 
 ## A Case Study
 
@@ -223,7 +226,7 @@ to worry too much about how `prep` is created (if you are interested, check
 out the `prepare_predictions` function). Instead, all you need to know is
 that parameters are stored in slot `dpars` and data are stored in slot `data`.
 Generally, parameters take on the form of a $S \times N$ matrix (with $S =$
-number of posterior samples and $N =$ number of observations) if they are
+number of posterior draws and $N =$ number of observations) if they are
 predicted (as is `mu` in our example) and a vector of size $N$ if the are not
 predicted (as is `phi`).
 

doc/brms_distreg.Rmd

@@ -40,7 +40,7 @@ model, in which we can specify predictor terms for all parameters of the assumed
 response distribution. In the vast majority of regression model implementations,
 only the location parameter (usually the mean) of the response distribution
 depends on the predictors and corresponding regression parameters. Other
-parameters (e.g., scale or shape parameters) are estimated as auxilliary
+parameters (e.g., scale or shape parameters) are estimated as auxiliary
 parameters assuming them to be constant across observations. This assumption is
 so common that most researchers applying regression models are often (in my
 experience) not aware of the possibility of relaxing it. This is understandable
@@ -74,8 +74,8 @@ linear predictor can be any real number.
 
 Unequal variance models are possibly the most simple, but nevertheless very
 important application of distributional models. Suppose we have two groups of
-patients: One group recieves a treatment (e.g., an antidepressive drug) and
-another group recieves placebo. Since the treatment may not work equally well
+patients: One group receives a treatment (e.g., an antidepressive drug) and
+another group receives placebo. Since the treatment may not work equally well
 for all patients, the symptom variance of the treatment group may be larger than
 the symptom variance of the placebo group after some weeks of treatment. For
 simplicity, assume that we only investigate the post-treatment values.
@@ -176,8 +176,8 @@ According to the parameter estimates, larger groups catch more fish, campers
 catch more fish than non-campers, and groups with more children catch less fish.
 The zero-inflation probability `zi` is pretty large with a mean of 41%. Please
 note that the probability of catching no fish is actually higher than 41%, but
-parts of this probability are already modeled by the poisson distribution itself
-(hence the name zero-*inflation*). If you want to treat all zeros as origniating
+parts of this probability are already modeled by the Poisson distribution itself
+(hence the name zero-*inflation*). If you want to treat all zeros as originating
 from a separate process, you can use hurdle models instead (not shown here).
 
 Now, we try to additionally predict the zero-inflation probability by the number

doc/brms_families.Rmd

@@ -94,13 +94,13 @@ $$
 with location parameter $\mu \in [0, 1]$ and positive shape parameter $\alpha$.
 -->
 
-## Survival models
+## Time-to-event models
 
-With survival models we mean all models that are defined on the positive reals
-only, that is $y \in \mathbb{R}^+$. The density of the **lognormal** family is
-given by
+With time-to-event models we mean all models that are defined on the positive
+reals only, that is $y \in \mathbb{R}^+$. The density of the **lognormal**
+family is given by
 $$
-f(y) = \frac{1}{\sqrt{2\pi}\sigma x} \exp\left(-\frac{1}{2}\left(\frac{\log(y) - \mu}{\sigma}\right)^2\right)
+f(y) = \frac{1}{\sqrt{2\pi}\sigma y} \exp\left(-\frac{1}{2}\left(\frac{\log(y) - \mu}{\sigma}\right)^2\right)
 $$ 
 where $\sigma$ is the residual standard deviation on the log-scale.
 The density of the **Gamma** family is given by
@@ -122,7 +122,15 @@ is set to $1$ for either the gamma or Weibull distribution. The density of the
 $$
 f(y) = \left(\frac{\alpha}{2 \pi y^3}\right)^{1/2} \exp \left(\frac{-\alpha (y - \mu)^2}{2 \mu^2 y} \right)
 $$
-where $\alpha$ is a positive shape parameter.
+where $\alpha$ is a positive shape parameter. The **cox** family implements Cox
+proportional hazards model which assumes a hazard function of the form $h(y) =
+h_0(y) \mu$ with baseline hazard $h_0(y)$ expressed via M-splines (which
+integrate to I-splines) in order to ensure monotonicity. The density of the cox
+model is then given by
+$$
+f(y) = h(y) S(y)
+$$
+where $S(y)$ is the survival function implied by $h(y)$.
 
 ## Extreme value models
 
@@ -154,20 +162,20 @@ $$
 f(y) = \frac{1}{2 \beta} \exp\left(\frac{1}{2 \beta} \left(2\xi + \sigma^2 / \beta - 2 y \right) \right) \text{erfc}\left(\frac{\xi + \sigma^2 / \beta - y}{\sqrt{2} \sigma} \right)
 $$
 where $\beta$ is the scale (inverse rate) of the exponential component, $\xi$ is
-the mean of the Gaussian componenent, $\sigma$ is the standard deviation of the
+the mean of the Gaussian component, $\sigma$ is the standard deviation of the
 Gaussian component, and $\text{erfc}$ is the complementary error function. We
 parameterize $\mu = \xi + \beta$ so that the main predictor term equals the
 mean of the distribution.
 
-Another family well suited for modelling response times is the
+Another family well suited for modeling response times is the
 **shifted_lognormal** distribution. It's density equals that of the
 **lognormal** distribution except that the whole distribution is shifted to the
 right by a positive parameter called *ndt* (for consistency with the **wiener**
 diffusion model explained below).
 
-A family concerned with the combined modelling of reaction times and
+A family concerned with the combined modeling of reaction times and
 corresponding binary responses is the **wiener** diffusion model. It has four
-model parameters each with a natural interpreation. The parameter $\alpha > 0$
+model parameters each with a natural interpretation. The parameter $\alpha > 0$
 describes the separation between two boundaries of the diffusion process, 
 $\tau > 0$ describes the non-decision time (e.g., due to image or motor processing),
 $\beta \in [0, 1]$ describes the initial bias in favor of the upper alternative,
@@ -273,7 +281,7 @@ $k$ for a subset of predictors. This leads to category specific
 effects (for details on how to specify them see `help(brm)`). Note that
 **cumulative** and **sratio** models use $\tau - \eta$, whereas **cratio** and
 **acat** use $\eta - \tau$. This is done to ensure that larger values of $\eta$
-increase the probability of *higher* reponse categories.
+increase the probability of *higher* response categories.
 
 The **categorical** family is currently only implemented with the multivariate
 logit link function and has density
@@ -294,7 +302,7 @@ function shown above.
 ## Zero-inflated and hurdle models
 
 **Zero-inflated** and **hurdle** families extend existing families by adding
-special processes for responses that are zero. The densitiy of a
+special processes for responses that are zero. The density of a
 **zero-inflated** family is given by
 $$
 f_z(y) = z + (1 - z) f(0) \quad \text{if } y = 0 \\