Use \diffvpredvar, and fix the PDF title that breaks the publish

_subfiles/exponential-families/_exm-uniform-not-exponential-family.qmd

@@ -1,5 +1,5 @@
 :::{#exm-uniform-not-exponential-family}
-#### The uniform distribution on $[0, \highend]$ is not an exponential family
+#### The uniform distribution on ${[0, \highend]}$ is not an exponential family
 
 <!-- no-figure: the example compares two density values at one point -->
 

_subfiles/logistic-inference/_cor-logistic-odds-ratio.qmd

@@ -12,18 +12,18 @@ $$
 
 ::: proof
 
-Let $\diff \vpredvar \eqdef \vpredvar' - \vpredvar$, so that $\vpredvar' = \vpredvar + \diff \vpredvar$, and the first entry of $\diff \vpredvar$ is $1 - 1 = 0$.
+Let $\diffvpredvar \eqdef \vpredvar' - \vpredvar$, so that $\vpredvar' = \vpredvar + \diffvpredvar$, and the first entry of $\diffvpredvar$ is $1 - 1 = 0$.
 
 $$
 \ba
 \orf{\vpredvar', \vpredvar}
 &= \frac{\oddsf{\vpredvar'}}{\oddsf{\vpredvar}}
 && \text{(definition of the odds ratio)}
 \\
-&= \frac{\oddsf{\vpredvar} \, \oddsfactorf{\diff \vpredvar}}{\oddsf{\vpredvar}}
+&= \frac{\oddsf{\vpredvar} \, \oddsfactorf{\diffvpredvar}}{\oddsf{\vpredvar}}
 && \text{(odds multiplier theorem)}
 \\
-&= \oddsfactorf{\diff \vpredvar}.
+&= \oddsfactorf{\diffvpredvar}.
 && \text{(divide numerator and denominator by } \oddsf{\vpredvar} > 0 \text{)}
 \ea
 $$

_subfiles/logistic-inference/_def-odds-multiplier.qmd

@@ -4,12 +4,12 @@
 Let:
 
 - $\vcoef$ be the coefficient vector of a [logistic regression model](#def-logistic-regression).
-- $\diff \vpredvar$ be a change in the [predictor](https://morrison-lab.github.io/pds/expectation.html#def-input) vector, whose first entry is $0$, because every predictor vector has first entry $1$.
+- $\diffvpredvar$ be a change in the [predictor](https://morrison-lab.github.io/pds/expectation.html#def-input) vector, whose first entry is $0$, because every predictor vector has first entry $1$.
 
-The **odds multiplier** of $\diff \vpredvar$ is the [exponential](https://morrison-lab.github.io/mds/algebra-exponentials.html#def-exponential-function) of the [dot product](https://morrison-lab.github.io/mds/linear-algebra-vectors.html#def-dot-product) of $\vcoef$ with $\diff \vpredvar$:
+The **odds multiplier** of $\diffvpredvar$ is the [exponential](https://morrison-lab.github.io/mds/algebra-exponentials.html#def-exponential-function) of the [dot product](https://morrison-lab.github.io/mds/linear-algebra-vectors.html#def-dot-product) of $\vcoef$ with $\diffvpredvar$:
 
 $$
-\oddsfactorf{\diff \vpredvar} \eqdef \e{\dprod{\vcoef}{\diff \vpredvar}}.
+\oddsfactorf{\diffvpredvar} \eqdef \e{\dprod{\vcoef}{\diffvpredvar}}.
 $$
 
 :::

_subfiles/logistic-inference/_exm-not-odds-multiplier.qmd

@@ -4,7 +4,7 @@
 
 In the [six-patient trial](#exm-logistic-regression), the [probability](https://morrison-lab.github.io/pds/probability-basics.html#def-probability) of recovery under the [maximum likelihood fit](intro-MLEs.qmd#def-mle) is $2/3$ in the treatment group and $1/3$ in the control group. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
 The code computes the [risk ratio](categorical-tests.qmd#def-risk-ratio) of treatment against control, <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
-and shows beside it the [odds multiplier](#def-odds-multiplier) of the change $\diff \vpredvar = \tp{\paren{0, 2}}$ from @exm-odds-multiplier.
+and shows beside it the [odds multiplier](#def-odds-multiplier) of the change $\diffvpredvar = \tp{\paren{0, 2}}$ from @exm-odds-multiplier.
 
 ```{r}
 #| code-fold: false

_subfiles/logistic-inference/_exm-odds-multiplier.qmd

@@ -2,7 +2,7 @@
 #### The odds multiplier of moving from control to treatment
 <!-- no-figure: the example computes a single number -->
 
-In the [six-patient trial](#exm-logistic-regression), moving a patient from the control group ($\predvar = -1$) to the treatment group ($\predvar = +1$) changes the predictor vector by $\diff \vpredvar = \tp{\paren{0, 2}}$. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
+In the [six-patient trial](#exm-logistic-regression), moving a patient from the control group ($\predvar = -1$) to the treatment group ($\predvar = +1$) changes the predictor vector by $\diffvpredvar = \tp{\paren{0, 2}}$. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
 The code computes the [odds multiplier](#def-odds-multiplier) of that change under the [maximum likelihood fit](intro-MLEs.qmd#def-mle).
 
 ```{r}

_subfiles/logistic-inference/_exm-thm-odds-multiplier.qmd

@@ -2,9 +2,9 @@
 #### The treated odds from the control odds
 <!-- no-figure: the example checks one product of two numbers -->
 
-In the [six-patient trial](#exm-logistic-regression), take $\vpredvar = \tp{\paren{1, -1}}$, a control patient, and $\diff \vpredvar = \tp{\paren{0, 2}}$, so that $\vpredvar' = \tp{\paren{1, 1}}$ is a treated patient. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
+In the [six-patient trial](#exm-logistic-regression), take $\vpredvar = \tp{\paren{1, -1}}$, a control patient, and $\diffvpredvar = \tp{\paren{0, 2}}$, so that $\vpredvar' = \tp{\paren{1, 1}}$ is a treated patient. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
 Under the [maximum likelihood fit](intro-MLEs.qmd#def-mle), the code computes the [odds](https://morrison-lab.github.io/pds/probability-basics.html#def-odds) of recovery at both [predictor](https://morrison-lab.github.io/pds/expectation.html#def-input) vectors,
-and the control odds times the [odds multiplier](#def-odds-multiplier) of $\diff \vpredvar$. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
+and the control odds times the [odds multiplier](#def-odds-multiplier) of $\diffvpredvar$. <!-- check-term-links: allow: "control" here is a trial arm, not a case-control control -->
 
 ```{r}
 #| code-fold: false

_subfiles/logistic-inference/_thm-odds-multiplier.qmd

@@ -4,13 +4,13 @@
 Let:
 
 - $\vpredvar$ be a [predictor](https://morrison-lab.github.io/pds/expectation.html#def-input) vector in the [logistic regression model](#def-logistic-regression) of @eq-logistic-model.
-- $\diff \vpredvar$ be a change in the predictor vector, with first entry $0$.
-- $\vpredvar' \eqdef \vpredvar + \diff \vpredvar$.
+- $\diffvpredvar$ be a change in the predictor vector, with first entry $0$.
+- $\vpredvar' \eqdef \vpredvar + \diffvpredvar$.
 
-Then the [odds](https://morrison-lab.github.io/pds/probability-basics.html#def-odds) of $\Outvar = 1$ at $\vpredvar'$ are the odds at $\vpredvar$ times the [odds multiplier](#def-odds-multiplier) of $\diff \vpredvar$:
+Then the [odds](https://morrison-lab.github.io/pds/probability-basics.html#def-odds) of $\Outvar = 1$ at $\vpredvar'$ are the odds at $\vpredvar$ times the [odds multiplier](#def-odds-multiplier) of $\diffvpredvar$:
 
 $$
-\oddsf{\vpredvar'} = \oddsf{\vpredvar} \, \oddsfactorf{\diff \vpredvar}.
+\oddsf{\vpredvar'} = \oddsf{\vpredvar} \, \oddsfactorf{\diffvpredvar}.
 $$
 
 :::
@@ -27,19 +27,19 @@ $$
 &= \e{\dprod{\vcoef}{\vpredvar'}}
 && \text{(log-odds of the model at } \vpredvar' \text{)}
 \\
-&= \e{\dprod{\vcoef}{\paren{\vpredvar + \diff \vpredvar}}}
+&= \e{\dprod{\vcoef}{\paren{\vpredvar + \diffvpredvar}}}
 && \text{(definition of } \vpredvar' \text{)}
 \\
-&= \e{\dprod{\vcoef}{\vpredvar} + \dprod{\vcoef}{\diff \vpredvar}}
+&= \e{\dprod{\vcoef}{\vpredvar} + \dprod{\vcoef}{\diffvpredvar}}
 && \text{(the dot product is linear in each slot)}
 \\
-&= \e{\dprod{\vcoef}{\vpredvar}} \, \e{\dprod{\vcoef}{\diff \vpredvar}}
+&= \e{\dprod{\vcoef}{\vpredvar}} \, \e{\dprod{\vcoef}{\diffvpredvar}}
 && \text{(} \e{a + b} = \e{a} \e{b} \text{)}
 \\
-&= \oddsf{\vpredvar} \, \e{\dprod{\vcoef}{\diff \vpredvar}}
+&= \oddsf{\vpredvar} \, \e{\dprod{\vcoef}{\diffvpredvar}}
 && \text{(log-odds of the model at } \vpredvar \text{)}
 \\
-&= \oddsf{\vpredvar} \, \oddsfactorf{\diff \vpredvar}.
+&= \oddsf{\vpredvar} \, \oddsfactorf{\diffvpredvar}.
 && \text{(definition of the odds multiplier)}
 \ea
 $$