FIX some typos in ipf and methodology vignette

vignettes/ipf.Rmd

@@ -17,7 +17,7 @@ knitr::opts_chunk$set(
 )
 ```
 
-This vignette explains the usage of the `ipf()` function, which has been used for calibrating the labour force survey of austria for several years.
+This vignette explains the usage of the `ipf()` function, which has been used for calibrating the labour force survey of Austria for several years.
 It is based on the Iterative Proportional Fitting algorithm and gives some flexibility about the details of the implementation. See [@mekogu2016] or `vignette("methodology")` for more details.
 
 ## Setup
@@ -45,7 +45,7 @@ We can see that this is currently not the case.
 xtabs(pWeight ~ gender, pop_sample)
 ```
 
-Due to random sampling (rather than stratified sampling), there are differences betweeen the gender distributions.
+Due to random sampling (rather than stratified sampling), there are differences between the gender distributions.
 We can pass `gender_distribution` as a parameter to `ipf()` to obtain modified weights.
 
 ```{r}
@@ -92,7 +92,7 @@ xtabs(pWeight ~ gender + age, pop_sample)
 ```
 
 Again, we can see that those constraints are not met.
-Suppliying the contingency table `con_ga` to `ipf()` will again resolve this.
+Supplying the contingency table `con_ga` to `ipf()` will again resolve this.
 
 ```{r}
 pop_sample_c2 <- ipf(pop_sample, conP = list(con_ga), w = "pWeight")

vignettes/methodology.Rmd

@@ -114,7 +114,7 @@ For ease of readability we will drop the subindices regarding strata $h$ and clu
 
 The uncalibrated bootstrap weights $\tilde{b}_j^{i}$ computed through the rescaled bootstrap procedure yields population statistics that differ from the known population margins of specified sociodemographic variables for which the base weights $w_j$ have been calibrated. To adjust for this the bootstrap weights $\tilde{b}_{j}^{i}$ can be recalibrated using iterative proportional fitting as described in [@mekogu2016].
 
-Let the original weight $w_{j}$ be calibrated for $n=n_P+n_H$ sociodemographic variables which are divided into the sets $\mathcal{P}:=\{p_{c}, c=1 \ldots,n_P\}$ and $\mathcal{H}:=\{h_{c}, c=1 \ldots,n_H\}$. $\mathcal{P}$ and $\mathcal{H}$ correspond to personal, for example gender or age, or household variables, like region or households size, respectively. Each variable in either $\mathcal{P}$ or $\mathcal{H}$ can take on $P_{c}$ or $H_{c}$ values with and $N^{p_c}_v$, $v=1,\ldots,P_c$, or $N^{h_c}_v$, $v=1,\ldots,H_c$, as the corresponding population margins. Starting with $k=0$ the iterative proportional fitting procedure is applied on each $\tilde{b}_j^{i}$, $i=1,\ldots, B$ seperately. The weights are first updated for personal and afterwards updated for household variables. If constraints regarding the populations margins are not met $k$ is raised by 1 and the procedure starts from the beginning. For the following denote as starting weight $\tilde{b}_j^{[0]}:=\tilde{b}_j^{i}$ for fixed $i$.
+Let the original weight $w_{j}$ be calibrated for $n=n_P+n_H$ sociodemographic variables which are divided into the sets $\mathcal{P}:=\{p_{c}, c=1 \ldots,n_P\}$ and $\mathcal{H}:=\{h_{c}, c=1 \ldots,n_H\}$. $\mathcal{P}$ and $\mathcal{H}$ correspond to personal, for example gender or age, or household variables, like region or households size, respectively. Each variable in either $\mathcal{P}$ or $\mathcal{H}$ can take on $P_{c}$ or $H_{c}$ values with and $N^{p_c}_v$, $v=1,\ldots,P_c$, or $N^{h_c}_v$, $v=1,\ldots,H_c$, as the corresponding population margins. Starting with $k=0$ the iterative proportional fitting procedure is applied on each $\tilde{b}_j^{i}$, $i=1,\ldots, B$ separately. The weights are first updated for personal and afterwards updated for household variables. If constraints regarding the populations margins are not met $k$ is raised by 1 and the procedure starts from the beginning. For the following denote as starting weight $\tilde{b}_j^{[0]}:=\tilde{b}_j^{i}$ for fixed $i$.
 
 ### Adjustment and trimming for $\mathcal{P}$
 
@@ -132,7 +132,7 @@ Since the sociodemographic variables $p_1,\ldots,p_{n_c}$ include person-specifi
 $$
   \tilde{b}_j^{[(n+1)k+n_p+1]} = \frac{{\sum\limits_{l\in a}} {\tilde{b}_l^{[(n+1)k+n_p]}}}{h_a}
 $$
-This can result in losing the population structure performed in the previouse subsection.
+This can result in losing the population structure performed in the previous subsection.
 
 ###  Adjustment and trimming for $\mathcal{H}$
 
@@ -160,7 +160,7 @@ $$
 \frac{N^{h_c}_v}{{\sum\limits_l} {\tilde{b}}_l^{[(n+1)k+j]}} \in ((1-\epsilon_h)N^{h_c}_v,(1+\epsilon_h)N^{h_c}_v)
 $$
 are verified, where the sum in the denominator expands over all observations which have the same value for variables $h_c$ or $p_c$.
-If these contraints hold true the algorithm reaches convergence, otherwise $k$ is raised by 1 and the procedure repeats itself.
+If these constraints hold true the algorithm reaches convergence, otherwise $k$ is raised by 1 and the procedure repeats itself.
 
 The above described calibration procedure is applied on each year $y_t$ of EU-SILC separately, $t=1,\ldots n_y$, thus resulting in so called calibrated bootstrap sample weights $b_{j}^{(i,{y_t})}$, $i=1,\ldots,B$ for each year $y$ and each household $j$.