LaTeX forum ⇒ MiKTeX and proTeXtWhat is wrong with my MikTex 2.8?

Information and discussion about MikTeX distribution for Windows and the related proTeXt: Installing, updating, configuring
harario
Posts: 7
Joined: Tue Feb 09, 2010 2:17 pm

What is wrong with my MikTex 2.8?

Postby harario » Tue Jun 08, 2010 12:40 pm

Hello folks,

I have MikTex 2.7 installed on my PC at home which works to perfection, and a 2.8 version installed on my office PC (Windows 2000) which gives me a constant headache. Virtually anytime I call a non-trivial package the file refuses to compile, although I have personally configured the system to install new packages automatically. I am a mere user and am not familiar with the intrinsic mechanism. I would provide any file needed in order for you to guide me through this.

Cheers,
Ofir

hesitz
Posts: 12
Joined: Mon Jun 07, 2010 2:32 am

Postby hesitz » Wed Jun 09, 2010 8:47 pm

I'm new to MikTex and I was having problems with documents where MikTex was supposed to be automatically installing packages as needed. Mine would also fail to compile when it was running across one of these packages. I don't have web link now, but I think my error was "Windows API Error 87" and the problem was apparently caused by MikTex somehow having two versions of itself running at the same time. The fix (or workaround) was to reboot the computer. I still occasionally have the problem, but a reboot seems to fix it.

harario
Posts: 7
Joined: Tue Feb 09, 2010 2:17 pm

Postby harario » Sun Jun 20, 2010 1:39 pm

Thanks for taking the trouble to reply!

Unfortunately, things don't seem to be as simple for me.
Below you can find my latex code.
I will attach the log shortly.
  1. \documentclass[12pt]{article}
  2.  
  3. \usepackage[cp1255]{inputenc}
  4. \usepackage{amsmath,amssymb, amsthm}
  5. \usepackage{ifpdf}
  6. \usepackage{color}
  7. \usepackage{graphicx}
  8. \usepackage{epsfig}
  9. \usepackage[bookmarks=false,colorlinks=true,linkcolor={blue},pdfstartview={XYZ null null 1}]{hyperref}
  10. \usepackage{vector}
  11. \usepackage{listings}
  12. \usepackage{verbatim}
  13. \usepackage{html,makeidx}
  14. \usepackage{booktabs}
  15. \usepackage{subfig}
  16. \usepackage{multirow}
  17. \usepackage{array}
  18. \usepackage{multicol}
  19.  
  20.  
  21.  
  22. \DeclareMathOperator{\Sp}{Sp}
  23.  
  24. \newcommand{\spc}{\hspace{2 mm}}
  25. \newcommand{\spcc}{\hspace{5 mm}}
  26. \newcommand{\real}{\mathbb{R}}
  27. \newcommand{\comp}{\mathbb{C}}
  28. \newcommand{\nat}{\mathbb{N}}
  29. \newcommand{\Q}{\mathbb{Q}}
  30. \newcommand{\Spc}{\hspace{10 mm}}
  31. \newcommand{\f}{\frac}
  32. \newcommand{\N}{\mathbb{N}}
  33. \newcommand{\F}{\mathbb{F}}
  34. \newcommand{\lmp}{\langle}
  35. \newcommand{\rmp}{\rangle}
  36. \renewcommand{\to}{\longrightarrow}
  37. \renewcommand{\iff}{\Leftrightarrow}
  38. \newcommand{\Aro}{\Rightarrow}
  39. \newcommand{\aro}{\rightarrow}
  40. \newcommand{\vo}{\{\overline{0}\}}
  41. \newcommand{\bv}[1]{\overline{#1}}
  42. \renewcommand{\a}{\alpha}
  43. \renewcommand{\b}{\beta}
  44. \newcommand{\ff}{\varphi}
  45. \newcommand{\bpm}{\begin{bmatrix}}
  46. \newcommand{\epm}{\end{bmatrix}}
  47. \newcommand{\bit}{\begin{itemize}}
  48. \newcommand{\eit}{\end{itemize}}
  49. \newcommand{\bn}[2]{\binom{#1}{#2}}
  50. \newcommand{\sm}[2]{\sum_{k=#1}^{#2}}
  51. \newcommand{\lr}[1]{\left(#1\right)}
  52. \newcommand{\str}[2]{\{^#1_#2\}}
  53. \newcommand{\cnt}[1]{\begin{center}#1\end{center}}
  54. \newcommand{\ld}{\ldots}
  55. \newcommand{\ve}{\varepsilon}
  56. \newcommand{\ub}{\uvec{\beta}}
  57. \newcommand{\uve}{\uvec{\varepsilon}}
  58. \newcommand{\e}{\text{\large{e}}}
  59. \newcommand{\di}{\mathrm{d}}
  60. \newcommand{\slfrac}[2]{\left.#1\middle/#2\right.}
  61.  
  62. \theoremstyle{plain}
  63. \newtheorem{theorem}{Theorem}[section]
  64.  
  65. \begin{document}
  66.  
  67. \begin{flushleft}
  68. {\small
  69. Ofir Harari \spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spc Generalized Linear Models \\
  70. ID 036335099 \spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spcc\spc Spring Semester 2010}
  71. \end{flushleft}
  72. \vspace{1em}
  73. \begin{center}
  74.  
  75. \underline{
  76. \textbf{\Large{$\cal{Final\spcc PROJECT}$}}
  77. }
  78. \end{center}
  79. \vspace{0.5em}
  80. \begin{enumerate}
  81. \item
  82. A hospital planed to carry out a medical study on a large sample of patients to investigate possible association between a certain disease D and patients' characteristics x (e.g. age, sex, smoking status, etc.). However, due to budget cuts it was decided to select a smaller sample from the original one. Let
  83. \begin{itemize}
  84. \item
  85. $D_i=1$ if the $i$-th patient has the disease, $Di=0$ otherwise
  86. \item
  87. $x_i$ - the vector of values for the $i$-th patient (fixed and known)
  88. \item
  89. $S_i=1$ if the $i$-th patient is selected to a smaller sample for the study, $S_i=0$ otherwise.
  90. \end{itemize}
  91. For the selected patients, logistic regression model has been fitted:
  92. \begin{align*}
  93. \log\frac{P\left(D_i=1\big|x_i,S_i=1\right)}{P\left(D_i=0\big|x_i,S_i=1\right)} = a+b'x_i\spc.
  94. \end{align*}
  95. Unless budget limitations, one would be naturally interested in fitting the logistic regression to the whole data set:
  96. \begin{align*}
  97. \log\frac{P\left(D_i=1\big|x_i\right)}{P\left(D_i=0\big|x_i\right)} = a^*+{b^*}'x_i\spc.
  98. \end{align*}
  99. \begin{enumerate}
  100. \item
  101. Suppose the proportion of chosen patients was the same among both groups (say, $r$). What is the connection between the coefficients in both models, i.e. between $a$, $b$ and $a^*$, $b^*$ ?
  102. \item
  103. Repeat the previous paragraph for the case where proportions of selected patients are different for patients with and without the disease (say, $P\left(S_i=1\big|D_i=1\right)=r_1$, while $P\left(S_i=1\big|D_i=0\right)=r_0)$.
  104. \item
  105. Comment the results and make conclusions. How will the decreased samle size affect the model fit?
  106. \end{enumerate}
  107. {\bf\underline{Solution}:}
  108. \begin{enumerate}
  109. \item
  110. Here
  111. \begin{align*}
  112. P\left(D_i=1\big|x_i,S_i=1\right)& = \frac{P\left(S_i=1\big|x_i,D_i=1\right)P\left(D_i=1\big|x_i\right)}{P\left(S_i=1\big|x_i\right)} = \\[1em]
  113. & = \frac{rP\left(D_i=1\big|x_i\right)}{r} = P\left(D_i=1\big|x_i\right)\spc.
  114. \end{align*}
  115. Similarly,\spc $P\left(D_i=0\big|x_i,S_i=1\right) = P\left(D_i=0\big|x_i\right)$ \spc and therefore, assuming the model is true
  116. \begin{align*}
  117. a+b'x_i &= \log\frac{P\left(D_i=1\big|x_i,S_i=1\right)}{P\left(D_i=0\big|x_i,S_i=1\right)} = \log\frac{P\left(D_i=1\big|x_i\right)}{P\left(D_i=0\big|x_i\right)} =\\[1em] & = a^*+{b^*}'x_i\spc,
  118. \end{align*}
  119. hence
  120. \begin{align*}
  121. X
  122. \left[
  123. \begin{array}{c}
  124. a - a^*\\
  125. b_1-b_1^*\\
  126. \vdots\\
  127. b_p-b_p^*
  128. \end{array}
  129. \right]
  130. =\underline{0}
  131. \end{align*}
  132. meaning (assuming $X$ is full-rank) $a=a^*$ and $b=b^*$ .
  133. \item
  134. Here
  135. \begin{align*}
  136. P\left(D_i=1\big|x_i,S_i=1\right)& = \frac{P\left(S_i=1\big|x_i,D_i=1\right)P\left(D_i=1\big|x_i\right)}{P\left(S_i=1\big|x_i\right)} = \\[1em]
  137. & = \frac{r_1P\left(D_i=1\big|x_i\right)}{r_0P\left(D_i=0\big|x_i\right)+r_1P\left(D_i=1\big|x_i\right)}
  138. \end{align*}
  139. and similarly
  140. \begin{align*}
  141. P\left(D_i=0\big|x_i,S_i=1\right) = \frac{r_0P\left(D_i=0\big|x_i\right)}{r_0P\left(D_i=0\big|x_i\right)+r_1P\left(D_i=1\big|x_i\right)}
  142. \end{align*}
  143. hence
  144. \begin{align*}
  145. a+b'x_i &= \log\frac{P\left(D_i=1\big|x_i,S_i=1\right)}{P\left(D_i=0\big|x_i,S_i=1\right)} = \log\frac{r_1P\left(D_i=1\big|x_i\right)}{r_0P\left(D_i=0\big|x_i\right)} =\\[1em]&= \log\frac{r_1}{r_0} + \log\frac{P\left(D_i=1\big|x_i\right)}{P\left(D_i=0\big|x_i\right)} = \log\frac{r_1}{r_0} + a^*+{b^*}'x_i\spc,
  146. \end{align*}
  147. and thus
  148. \begin{align*}
  149. X
  150. \left[
  151. \begin{array}{c}
  152. a - a^* - \log\dfrac{r_1}{r_0}\\
  153. b_1-b_1^*\\
  154. \vdots\\
  155. b_p-b_p^*
  156. \end{array}
  157. \right]
  158. =\underline{0}\spc,
  159. \end{align*}
  160. and again, going by the assumption that $X$ is full-rank, we have
  161. \begin{align*}
  162. a=a^*+\log\dfrac{r_1}{r_0}\spcc \text{and}\spcc b=b^* \spc.
  163. \end{align*}
  164. \item
  165. From previous paragraphs it is clear that if our objective is to identify the major factors that affect the probability to become diseased sampling makes no difference. The same goes for Odds Ratio, seeing as the intercepts cancell each other out.
  166.  
  167. If, however, we aim to make a prediction about the probability of a prticular subject, uneven sampling would result in larger estimates in favor of the over-sampled group.
  168.  
  169. Figure \ref{1.Simulation} shows the results of a simulation we performed, which contained an indepedent variable $x$ ($500$ draws from a $\mathrm{U}(0,1)$ distribution) and a dependent variable
  170. \begin{align*}
  171. D\sim \text{{\large $\mathrm{Binom}$}}\left(1,\dfrac{\exp\left\{0.3x-0.5\right\}}{1+\exp\left\{0.3x-0.5\right\}}\right)\spcc.
  172. \end{align*}
  173.  
  174. The logistic model is then fitted for the complete set of data, and thereafter refitted for the partial data, where in the first time $r_0=r_1=0.8$ and in the second time $r_0 = 0.9$ and $r_1 = 0.65$.
  175.  
  176. In Figure \ref{1.Simulation} one can see how $\hat{\beta}_1 - \hat{\beta}_1^*$ is centered at $0$ no matter the sampling ratios, while the uneven sampling moves $\beta_0 - \beta_0^*$ about $\log\dfrac{0.9}{0.65} = 0.325$ .
  177.  
  178. The simulation code follows:
  179. {\scriptsize
  180. \begin{lstlisting}
  181. n <- 500
  182. X <- runif(n)
  183. D <- rep(0,n)
  184. p <- exp(0.3*X - 0.5)/(1+exp(0.3*X-0.5))
  185. for(i in 1:n)
  186. {
  187. D[i] <- rbinom(1,1,p[i])
  188. }
  189.  
  190.  
  191. Coeff.Compar <- function(k,r0,r1)
  192. {
  193. k <- 2000
  194. d0 <- rep(0,k)
  195. d1 <- rep(0,k)
  196.  
  197. for(j in 1:k)
  198. {
  199. true <- glm(D~X, family=binomial)
  200. beta.true <- true$coeff
  201. rand <- 1:length(D[D==0])
  202. index <- sample(rand,length(D[D==0])*r0)
  203. Select <- rep(0,length(D[D==0]))
  204. Select[index] <- 1
  205. samp0 <- data.frame(cbind(X=X[D==0][Select==1],
  206. D=D[D==0][Select==1]))
  207. names(samp0) <- c("X","D")
  208. rand <- 1:length(D[D==1])
  209. index <- sample(rand, length(D[D==1])*r1)
  210. Select <- rep(0, length(D[D==1]))
  211. Select[index] <- 1
  212. samp1 <- data.frame(cbind(X=X[D==1][Select==1],
  213. D=D[D==1][Select==1]))
  214. names(samp1) <- c("X", "D")
  215. samp <- rbind(samp0,samp1)
  216. sampled <- glm(samp$D ~ samp$X, family = binomial)
  217. beta.sampled <- sampled$coeff
  218.  
  219. d0[j] <- beta.true[1] - beta.sampled[1]
  220. d1[j] <- beta.true[2] - beta.sampled[2]
  221. }
  222. return(d0,d1)
  223. }
  224.  
  225. sim1 <- Coeff.Compar(1000,0.8,0.8)
  226. sim2 <- Coeff.Compar(1000,0.9,0.65)
  227.  
  228. windows(record=TRUE, width=30, height=20)
  229. par(mfrow = c(2,2))
  230. hist(sim1$d0, main="", xlab="")
  231. title(main=expression(beta[0]-beta[0]^"*"), cex.main=1.8,
  232. sub=expression(r[0]==r[1]~"=0.8"),cex.sub=1.8)
  233. hist(sim1$d1, main="", xlab="")
  234. title(main=expression(beta[1]-beta[1]^"*"), cex.main=1.8,
  235. sub=expression(r[0]==r[1]~"=0.8"), cex.sub=1.8)
  236. hist(sim2$d0, main="", xlab="")
  237. title(main=expression(beta[0]-beta[0]^"*"), cex.main=1.8,
  238. sub=expression(r[0]==0.9~" , "~r[1]==0.65), cex.sub=1.8)
  239. hist(sim2$d1, main="", xlab="")
  240. title(main=expression(beta[1]-beta[1]^"*"), cex.main=1.8,
  241. sub=expression(r[0]==0.9~" , "~r[1]==0.65), cex.sub=1.8)
  242. \end{lstlisting}
  243. }
  244.  
  245. \begin{figure}[ht]
  246. \begin{center}
  247. \includegraphics[width=1\textwidth]{1.Simulation.eps}
  248. \end{center}
  249. \caption{Simulation results for $\beta_0 - \beta_0^*$ and $\beta_1 - \beta_1^*$ both when $r_0=r_1$ and when $r_0\ne r_1$}
  250. \label{1.Simulation}
  251. \end{figure}
  252.  
  253. \clearpage
  254.  
  255. \end{enumerate}
  256.  
  257. \item
  258. The data below are the number of cases of lung cancer and the number of ``man-years at risk'' in a very large British study of smoking men and its effect on lung cancer. The table is classified by number of years of smoking in five-year intervals, beginning at $15$-$19$ and up to $55$-$59$, and equivalent number of cigarettes smoked per day, in intervals as shown in the Table below. The data are in the form $r/n$, where $r$ is the number of lung cancer cases and $n$ the number of men at risk.
  259. \begin{center}
  260. {\footnotesize
  261. \begin{tabular}{l{c}cccccc}
  262. &Years smoking &\multicolumn{6}{c}{Cigs/day} \\
  263. \midrule
  264. & &$1$-$9$ &$10$-$14$ &$15$-$19$ &$20$-$24$ &$25$-$34$ &$35+$\\
  265. \midrule
  266. &$15$-$19$ &0/3121 &0/3577 &0/4317 &0/5683 &0/3042 &0/670\\
  267. \midrule
  268. &$20$-$24$ &0/2937 &1/3286 &0/4214 &1/6385 &1/4050 &0/1166\\
  269. \midrule
  270. &$25$-$29$ &0/2288 &1/2546 &0/3185 &1/5483 &4/4290 &0/1482\\
  271. \midrule
  272. &$30$-$34$ &0/2015 &1/2219 &4/2560 &6/4687 &9/4268 &4/1580\\
  273. \midrule
  274. &$35$-$39$ &1/1648 &0/1826 &0/1893 &5/3646 &9/3529 &6/1336\\
  275. \midrule
  276. &$40$-$44$ &2/1310 &1/1886 &2/1334 &12/2411 &11/2424 &10/924\\
  277. \midrule
  278. &$45$-$49$ &0/927 &2/988 &2/849 &9/1567 &10/1409 &7/556\\
  279. \midrule
  280. &$50$-$54$ &3/710 &4/684 &2/470 &7/857 &5/663 &4/255\\
  281. \midrule
  282. &$55$-$59$ &0/606 &3/449 &5/280 &7/416 &3/284 &1/104\\
  283. \midrule
  284. \end{tabular}
  285. }
  286. \end{center}
  287. \begin{enumerate}
  288. \item
  289. For these data, find a well-fitting parsimonious model relating the proportion suffering from lung cancer to smoking rate and years of smoking. Give the interpretation of your model in terms of the risk of developing lung cancer.
  290. \item
  291. What are the chances of developing lung cancer for a man smoking 20 cigarettes per day for the last 40 years? (give a pointwise estimate and the corresponding confidence interval).
  292. \end{enumerate}
  293. {\bf\underline{Solution}:}
  294. \begin{enumerate}
  295. \item
  296. All model selection methods lead to the Main Effect binomial model:
  297. \begin{align*}
  298. \log\frac{p_i}{1-p_i} = \beta_0 + \beta_{1,\ldots,9}\text{YearsSmok}_i + \beta_{10,\ldots,15}\text{CigsPerDay}_i\spc.
  299. \end{align*}
  300. The residuals of this fit can be seen in Figure \ref{2.ME.Resid}, ANOVA table is
  301. {\scriptsize
  302. \begin{lstlisting}
  303. Df Deviance Resid. Df Resid. Dev P(>|Chi|)
  304. NULL 53 358.77
  305. Years_Smk 8 258.78 45 99.99 2.372e-51
  306. Cigs_per_Day 5 60.53 40 39.46 9.448e-12
  307. \end{lstlisting}
  308. }
  309. \begin{figure}[ht]
  310. \begin{center}
  311. \includegraphics[width=1\textwidth]{2.ME.Resid.eps}
  312. \end{center}
  313. \caption{Residuals for the Main-Effect Model}
  314. \label{2.ME.Resid}
  315. \end{figure}
  316. and goodness of fit test yields $\text{p-value} = 0.494$ for $D=39.465$ on $\mathrm{df} = 40$. All in all a lovely fit, except for its lack of interpretability, and the statistical insignificance of most of the coefficients of the different levels as stand-alone variables.\\[0.5em]
  317.  
  318. To take care of these issues, we proceed to treat both independent variables as continuous. this is done by
  319. {\scriptsize
  320. \begin{lstlisting}
  321. Yrs_Smoke <- Years_Smk
  322. levels(Yrs_Smoke) <- c("0","1","2","3","4","5","6","7","8")
  323. Yrs_Smk <- as.numeric(as.character(Yrs_Smoke))
  324.  
  325. Cigs_Day <- Cigs_per_Day
  326. levels(Cigs_Day) <- c("0","1","2","3","4","5")
  327. Cig_Day <- as.numeric(as.character(Cigs_Day))
  328. \end{lstlisting}
  329. }
  330.  
  331. and we can therefore fit
  332. \begin{align*}
  333. \log\frac{p_i}{1-p_i} = \beta_0 + \beta_1\text{YrsSmk}_i + \beta_2\text{CigDay}_i\spc.
  334. \end{align*}
  335.  
  336. This idea is motivated by Figure \ref{2.Cont.Logits}, where both continuous predictors are shown against $p$ in the log-scale.
  337. The results of this fit can be seen in
  338. {\scriptsize
  339. \begin{lstlisting}
  340. Call:
  341. glm(formula = cbind(Cases, At_Risk - Cases) ~ Yrs_Smk + Cig_Day,
  342. family = binomial)
  343.  
  344. Coefficients:
  345. Estimate Std. Error z value Pr(>|z|)
  346. (Intercept) -10.03960 0.29838 -33.647 < 2e-16 ***
  347. Yrs_Smk 0.56570 0.03847 14.704 < 2e-16 ***
  348. Cig_Day 0.43653 0.05764 7.573 3.64e-14 ***
  349.  
  350. Null deviance: 358.771 on 53 degrees of freedom
  351. Residual deviance: 59.035 on 51 degrees of freedom
  352. \end{lstlisting}
  353. }
  354.  
  355. \begin{figure}[ht]
  356. \begin{center}
  357. \includegraphics[width=1\textwidth]{2.Cont.Logits.eps}
  358. \end{center}
  359. \caption{Years of Smoking and Cigarettes per Day in the logit scale}
  360. \label{2.Cont.Logits}
  361. \end{figure}
  362.  
  363. Comparing the main-effect model with the current one, we have
  364. {\scriptsize
  365. \begin{lstlisting}
  366. Model 1: cbind(Cases, At_Risk-Cases)~Yrs_Smk+Cig_Day
  367. Model 2: cbind(Cases, At_Risk-Cases)~Years_Smk+Cigs_per_Day
  368. Resid. Df Resid. Dev Df Deviance P(>|Chi|)
  369. 1 51 59.035
  370. 2 40 39.465 11 19.570 0.052
  371. \end{lstlisting}
  372. }
  373.  
  374. which is borderline-significant, but we will let ourselves enjoy the benefit of the doubt, seeing as the goodness of fit is sufficiently good, with $\text{p-value} = 0.205$ for $D=59.035$ on $\mathrm{df} = 51$.\\[0.5em]
  375.  
  376. Taking it one step further, we would like to test
  377. \begin{align*}
  378. {\cal{H}}:\beta_0 = -10\spc;\spc \beta_1 = \beta_2 = \frac{1}{2}\spcc.
  379. \end{align*}
  380. We do that by denoting \spc$\mathrm{Score}_i = \mathrm{YrsSmk}_i + \mathrm{CigDay}_i$\spc and comparing the deterministic model
  381. \begin{align*}
  382. \log\frac{p_i}{1-p_i} = \frac{1}{2}\text{Score}_i - 10\spc.
  383. \end{align*}
  384. to the previous model. Doing so, we learn that
  385. {\scriptsize
  386. \begin{lstlisting}
  387. Model 1: cbind(Cases, At_Risk-Cases)~offset(-10+0.5*score)-1
  388. Model 2: cbind(Cases, At_Risk-Cases)~Yrs_Smk+Cig_Day
  389. Resid. Df Resid. Dev Df Deviance P(>|Chi|)
  390. 1 54 64.465
  391. 2 51 59.035 3 5.430 0.143
  392. \end{lstlisting}
  393. }
  394. and also the goodness of fit test yields $\text{p-value} = 0.156$ with $\mathrm{df}=54$ and $D=64.46$ , and so we are quite happy with the model we ended up having.\\[0.5em]
  395. Figure \ref{2.Score.Logit} displays the newly-introduced Score variable against the logit of the empirical probabilities. This hints that opting for a univariate Score model cannot be completely ruled out, although it is far from perfect, as implied from the residuals plotted in Figure \ref{2.Score.Resid}.
  396.  
  397. \begin{figure}[ht]
  398. \begin{center}
  399. \includegraphics[width=0.65\textwidth]{2.Score.Logit.eps}
  400. \end{center}
  401. \caption{The Score variable in the logit scale}
  402. \label{2.Score.Logit}
  403. \end{figure}
  404.  
  405. \begin{figure}[ht]
  406. \begin{center}
  407. \includegraphics[width=0.9\textwidth]{2.Score.Resid.eps}
  408. \end{center}
  409. \caption{Residuals for the Score model}
  410. \label{2.Score.Resid}
  411. \end{figure}
  412.  
  413. The Score model is very easy to interpret if we consider years of smoking and smoking rate as equally-contributive to the risk of having lung-cancer. Taking $1/(1+\e^{10})$ to be the probability of a non-smoker to get lung cancer, the odds-ratio goes up $\e^{0.5}$ units whenever one climbs up the scale in either factor.
  414.  
  415. \item
  416. As aesthetically pleasing as our model is, it contains no stochastic elements, due to the fixation of both coefficients in the end of the previous paragraph. We therefore accept the Score model as a qualitative instrument, giving us a clear insight of the nature of the influence of smoking on lung cancer, but retreat to the main-effect model for predictions, confidence intervals etc.\\[0.5em]
  417. Using R's \textit{predict.glm($\cdot$)} function we can have, for example, all point estimates and $95\%$ confidence intervals for men who have been smoking for $40$-$44$ years:
  418. {\footnotesize
  419. \begin{lstlisting}
  420. Cig_Day score P.Obs P.Exp P.Low P.Up
  421. 1-9 5 0.00153 0.00079 0.00033 0.00186
  422. 10-14 6 0.00053 0.00177 0.00098 0.00321
  423. 15-19 7 0.00150 0.00233 0.00130 0.00417
  424. 20-24 8 0.00498 0.00420 0.00281 0.00627
  425. 25-34 9 0.00454 0.00519 0.00353 0.00763
  426. 35+ 10 0.01082 0.00845 0.00544 0.01311
  427. \end{lstlisting}
  428. }
  429.  
  430. Therefore, for a $20$ cigarettes a day smoker, who has been having this bad habit for the last $40$ years, a point estimate for the probability to have lung cancer would be $0.42\%$ , with a $95\%$ confidence interval of $(0.28\%,0.63\%)$ .
  431.  
  432. \begin{figure}[ht]
  433. \begin{center}
  434. \includegraphics[width=0.75\textwidth]{2.ME.Predict.eps}
  435. \end{center}
  436. \caption{Confidence bands for the probability for lung cancer conditioned on each of the independent variables in the Main-Effect model}
  437. \label{2.ME.Predict}
  438. \end{figure}
  439.  
  440. An illustration of the point estimates and the confidence bands for the relevant sector, projected on both predictors, is in display in Figure \ref{2.ME.Predict}.
  441.  
  442. \begin{comment}
  443. \begin{figure}[ht]
  444. \begin{center}
  445. \includegraphics[width=1\textwidth]{2.Exp.Obs.eps}
  446. \end{center}
  447. \caption{Predictions vs. empirical probabilities along Score for the Main-Effect and final Score model}
  448. \label{2.Exp.Obs}
  449. \end{figure}
  450. \end{comment}
  451. \end{enumerate}
  452.  
  453. \clearpage
  454.  
  455. \item
  456. In a study male and female drivers were interviewed about the importance of various features of vehicle safety to them when they were buying a car. Table below shows the ratings for air conditioning according to the sex and age of the driver.
  457.  
  458. \begin{center}
  459. {\footnotesize
  460. \begin{tabular}{l{c}cccc}
  461. &Sex &Age &No or little Importance &Important &Very Important\\
  462. \midrule
  463. &\multirow{3}{*}{Women} &18-23 &$26$ &$12$ &$7$\\
  464.  
  465. & &24-40 &9 &21 &15\\
  466.  
  467. & &$>40$ &5 &14 &41\\
  468. \midrule
  469. &\multirow{3}{*}{Men} &18-23 &40 &17 &8\\
  470.  
  471. & &24-40 &17 &15 &12\\
  472.  
  473. & &$>40$ &8 &15 &18\\
  474. \midrule
  475. &Total & &105 &94 &101\\
  476. \midrule
  477. \end{tabular}
  478. }
  479. \end{center}
  480.  
  481. \begin{enumerate}
  482. \item
  483. Look at the data and try to make some preliminary conclusions (conjectures?).
  484. \item
  485. Fit an appropriate model for these data. Do the ratings change with the age similarly in both sex groups? Does sex influence at all? Can you say that the ratings do not change with the age?
  486. \item
  487. In fact, the response variable for these data is an \textit{ordinal} categorical variable. Exploit this fact and fit the corresponding proportional odds logistic model. Is it an adequate model for the data?
  488. \item
  489. Return to all the questions from the second paragraph.
  490. \item
  491. Compare the results from both models. In particular, compare the estimated probabilities with the observed proportions. Make final conclusions and comment the results of the study.
  492. \end{enumerate}
  493.  
  494. {\bf\underline{Solution}:}
  495. \begin{enumerate}
  496. \item
  497. Looking at Figure \ref{3.Prob.Crude}, it is quite clear that the probabilities of a random subject (be it male or female) follow different pathes, suggesting we cannot bin together any two groups. It is also of note that the trend in the ``Important'' group is different for men and women, meaning the ``Sex'' factor is likely to be statistically significant.
  498.  
  499. \begin{figure}[ht]
  500. \begin{center}
  501. \includegraphics[width=0.9\textwidth]{3.Prob.Crude.eps}
  502. \end{center}
  503. \caption{Early examination of the data}
  504. \label{3.Prob.Crude}
  505. \end{figure}
  506.  
  507. \item
  508. Fitting the multinomial model
  509. \begin{align*}
  510. \log\left(\frac{P_{{ji}}}{P_{{\text{NotImp},i}}}\right) = \beta_{0j} + \beta_{1j}\mathrm{Sex}_i + \beta_{2j}\mathrm{Age}_i\spc;\spc j = \text{Imp},\text{VeryImp}
  511. \end{align*}
  512. we have
  513. {\scriptsize
  514. \begin{lstlisting}
  515. Call:
  516. multinom(formula = cbind(No_Imp, Imp, Very_Imp) ~ Sex + Age)
  517.  
  518. Coefficients:
  519. (Intercept) SexM Age18-23 Age24-40
  520. Imp 0.996906 -0.3881235 -1.587705 -0.4594416
  521. Very_Imp 1.877669 -0.8130098 -2.916737 -1.4386386
  522.  
  523. Residual Deviance: 580.7022
  524. AIC: 596.7022
  525. \end{lstlisting}
  526. }
  527. and knowing the shortcomings of R's deviance calculation in this kind of models, we use our own routine
  528. {\scriptsize
  529. \begin{lstlisting}
  530. Obs <- cbind(No_Imp,Imp, Very_Imp)
  531. Exp <- Total*model1$fitted.values
  532. Chi <- sum((Obs - Exp)^2/Exp)
  533. d.first <- ifelse(Obs == 0, 0, Obs*log(Obs/Exp))
  534. dev <- 2*sum(d.first)
  535. df <- length(Sex)*2 - model1$edf
  536. 1 - pchisq(dev, df)
  537. \end{lstlisting}
  538. }
  539. To obtain $\text{p-value}=0.414$ for $D=3.939$ on $\mathrm{df}=4$. A visualization of the multinomial fit is in display in Figure \ref{3.Multinom}, along with the empirical probabilities for the different groups.
  540.  
  541. \begin{figure}[ht]
  542. \begin{center}
  543. \includegraphics[width=1\textwidth]{3.Multinom.eps}
  544. \end{center}
  545. \caption{Observed probabilities along with the fitted ones (thin solid lines) for the Multinomial model}
  546. \label{3.Multinom}
  547. \end{figure}
  548.  
  549. From the summary, the ``Not Important'' initial rate is higher among men than among women, whereas the opposite is true for the other groups. This pattern is maintained in the ``Not Important'' and ``Very Important'' groups. In the ``Important'' group, however, there is a reversal of trends, and older man belong to this group more often than their female counterparts (obviously, women tend to suffer heat waves midway-through their $40$'s, making ``Very important'' a more obvious choice).\\[0.5em]
  550.  
  551. To make the importance of ``Sex'' official, let us compare our model with a nested one, containing no ``Sex'' factor:
  552. {\scriptsize
  553. \begin{lstlisting}
  554. Likelihood ratio tests of Multinomial Models
  555.  
  556. Response: cbind(No_Imp, Imp, Very_Imp)
  557. Model Resid.df Resid.Dev Test Df LR stat. Pr(Chi)
  558. Age 6 587.2074
  559. Sex + Age 4 580.7022 1 vs 2 4 26.505178 0.03867396
  560. \end{lstlisting}
  561. }
  562. and we see ``Sex'' is rather influential.\\[0.5em]
  563.  
  564. Repeating for ``Age'':
  565. {\scriptsize
  566. \begin{lstlisting}
  567. Likelihood ratio tests of Multinomial Models
  568.  
  569. Response: cbind(No_Imp, Imp, Very_Imp)
  570. Model Resid.df Resid.Dev Test Df LR stat. Pr(Chi)
  571. Sex 8 646.2812
  572. Sex + Age 4 580.7022 1 vs 2 4 65.579 1.942890e-13
  573. \end{lstlisting}
  574. }
  575.  
  576. \item
  577. Fitting the Proportional Odds model
  578. \begin{align*}
  579. \log\frac{P\left(y\leq y_j\big|\text{Sex}_i,\text{Age}_i\right)}{P\left(y > y_j\big|\text{Sex}_i,\text{Age}_i\right)} = \beta_{0j} + \beta_{1}\mathrm{Sex}_i + \beta_{2}\mathrm{Age}_i
  580. \end{align*}
  581.  
  582. we have Figure \ref{3.Prop.Odds} and
  583.  
  584. \begin{figure}[ht]
  585. \begin{center}
  586. \includegraphics[width=1\textwidth]{3.Prop.Odds.eps}
  587. \end{center}
  588. \caption{Observed probabilities along with the fitted ones (thin solid lines) for the Proportional Odds model}
  589. \label{3.Prop.Odds}
  590. \end{figure}
  591.  
  592. {\scriptsize
  593. \begin{lstlisting}
  594. Call:
  595. polr(formula = factor(Rating) ~ Age1 + Sex1)
  596.  
  597. Coefficients:
  598. Value Std. Error t value
  599. Age1 1.1164159 0.1457415 7.660246
  600. Sex1 -0.5769928 0.2261076 -2.551850
  601.  
  602. Intercepts:
  603. Value Std. Error t value
  604. A|B 0.5725 0.4662 1.2281
  605. B|C 2.1838 0.4862 4.4920
  606.  
  607. Residual Deviance: 581.3124
  608. AIC: 589.3124
  609. \end{lstlisting}
  610. }
  611.  
  612. The true deviance for this model is $D=4.549$ on $\mathrm{df}=12$, giving $\text{p-value}=0.97$ for a terrific goodness of fit.
  613.  
  614. \item
  615. From the t-values in the summary table of the proportional-odds model it looks like both factors are significant again. To be on the safe side, we chech this again by
  616. {\scriptsize
  617. \begin{lstlisting}
  618. Likelihood ratio tests of ordinal regression models
  619.  
  620. Response: factor(Rating)
  621. Model Resid.df Resid.Dev Test Df LR stat. Pr(Chi)
  622. Age1 297 587.8542
  623. Age1 + Sex1 296 581.3124 1 vs 2 1 6.541726 0.01053730
  624. \end{lstlisting}
  625. }
  626. and
  627. {\scriptsize
  628. \begin{lstlisting}
  629. Model Resid.df Resid.Dev Test Df LR stat. Pr(Chi)
  630. Sex1 297 646.2848
  631. Age1 + Sex1 296 581.3124 1 vs 2 1 64.97237 7.771561e-16
  632. \end{lstlisting}
  633. }
  634. and we are left with the exact same conclusions.
  635. \item
  636. Judging on Figures \ref{3.Multinom} and \ref{3.Prop.Odds}, it is hard to tell which model is better: the multinomial fit seems to suit better the female group while the proportional odds model is perhaps slightly better for the males. We give the edge to the proportional odds model for its simplicity (less parameters to be estimated) and exceptional goodness of fit. The increase in the proportion of men in the ``Important'' group over age is not reflected in either model, but the proportional-odds model seems to do a little more justice with this phenomenon.
  637. \end{enumerate}
  638.  
  639. \clearpage
  640. \item
  641. The data set {\color{blue}{\textit{kyphosis}}} in available in the library \textit{rpart} and contains the data on $81$ children who have had corrective spinal surgery. The binary outcome \textit{Kyphosis} indicate presence absence of postoperative deformity called kyphosis. The three explanatory variables are age in months (\textit{Age}), the number of vertebrae involved (\textit{Number}) and the number of the first (topmost) vertebra operated on (\textit{Start}).
  642. \begin{enumerate}
  643. \item
  644. Fit the logit main effects model. Does it seem adequate to the data? What can you suggest to improve the model?
  645. \item
  646. Add quadratic terms, try to add iteractions (if necessary) and remove unsignificant terms. Are all the explanatory variables significant? Comment on the resulting model and compare it with the main effects one.
  647. \item
  648. Fit the nonparametric additive model (gam) using the explanatory variables you have found significant on the previous steps. Plot the resulting curves, comment the results.
  649. \item
  650. Make final (?) conclusions.
  651. \end{enumerate}
  652.  
  653. {\bf\underline{Solution}:}
  654. \begin{enumerate}
  655. \item
  656.  
  657. \begin{figure}[ht]
  658. \begin{center}
  659. \includegraphics[width=1\textwidth]{4.ME.Resid.eps}
  660. \end{center}
  661. \caption{Residuals for the Main-Effect logit binary model}
  662. \label{4.ME.Resid}
  663. \end{figure}
  664.  
  665. \item
  666.  
  667. \begin{figure}[ht]
  668. \begin{center}
  669. \includegraphics[width=1\textwidth]{4.Step.Resid.eps}
  670. \end{center}
  671. \caption{Residuals for the logit binary model obtained by applying Stepwise Regression}
  672. \label{4.Step.Resid}
  673. \end{figure}
  674.  
  675. \item
  676.  
  677. \begin{figure}[ht]
  678. \begin{center}
  679. \includegraphics[width=0.83\textwidth]{4.Spline.eps}
  680. \end{center}
  681. \caption{Plots for the general additive nonparametric model}
  682. \label{4.Spline}
  683. \end{figure}
  684.  
  685.  
  686. \item
  687.  
  688. \end{enumerate}
  689.  
  690. \item
  691. In an experiment to investigate the social behavior of hornets, different numbers of hornets were placed in boxes, and the number of cells built by the hornets was counted. Below are given the data from $38$ boxes: the number of cells built for each number of hornets.
  692. \begin{center}
  693. {\small
  694. \begin{tabular}{l{c}l}
  695. &$\#$ Hornets &\makebox[1.5in]{$\#$ Cells}\\
  696. \midrule
  697. &1 &0, 1, 2, 2, 4, 4, 5, 10, 11, 18\\
  698. &2 &0, 4, 5, 7, 8, 13, 18, 29\\
  699. &5 &7, 8, 17, 18, 19\\
  700. &6 &17\\
  701. &10 &12, 17, 18, 23, 25, 32\\
  702. &16 &12\\
  703. &19 &23\\
  704. &20 &21, 23, 30, 31\\
  705. &41 &30
  706. \end{tabular}
  707. }
  708. \end{center}
  709. \begin{enumerate}
  710. \item
  711. Assuming a normal model with constant variance, find the appropriate transformation of $\#\text{Cells}$ using $\#\text{Hornets}$ or $\log(\#\text{Hornets})$ as explanatory variable. Analyse the results of fitting and point out problems you have found (if any).
  712. \item
  713. Consider the previous model but allow heterogeneity for variance assuming that it is also a function of $\#\text{Hornets}$ or $\log(\#\text{Hornets})$ respectively. Compare your final model with that from the previous paragraph. Is the assumption of equal variances reasonable?
  714. \item
  715. Assume the Poisson model for $\#\text{Cells}$ and fit the corresponding regression model for $\#\text{Hornets}$ or $\log(\#\text{Hornets})$. Comment on the fit of the Poisson model, and compare the results with those from previous paragraphs. Is there overdispersion? If ``yes'', modify your original Poisson model. Make final conclusions.
  716. \end{enumerate}
  717.  
  718. {\bf\underline{Solution}:}
  719. \begin{enumerate}
  720. \item
  721. \begin{figure}[ht]
  722. \begin{center}
  723. \includegraphics[width=0.8\textwidth]{5.Initial.eps}
  724. \end{center}
  725. \caption{Early examination of the data}
  726. \label{5.Initial}
  727. \end{figure}
  728.  
  729.  
  730. \begin{figure}[ht]
  731. \begin{center}
  732. \includegraphics[width=1\textwidth]{5.Boxcox.eps}
  733. \end{center}
  734. \caption{Box-Cox log-likelihood plots for both No. Hornets and $\log(\text{No. Hornets})$ as independent variables}
  735. \label{5.Boxcox}
  736. \end{figure}
  737.  
  738. \begin{figure}[ht]
  739. \begin{center}
  740. \includegraphics[width=1\textwidth]{5.Lin.Resid.eps}
  741. \end{center}
  742. \caption{Residuals for the homogeneous variance model with No. Hornets as the predictor}
  743. \label{5.Lin.Resid}
  744. \end{figure}
  745.  
  746.  
  747. \begin{figure}[ht]
  748. \begin{center}
  749. \includegraphics[width=1\textwidth]{5.log.Resid.eps}
  750. \end{center}
  751. \caption{Residuals for the homogeneous variance model with $\log(\text{No. Hornets})$ as the predictor}
  752. \label{5.log.Resid}
  753. \end{figure}
  754.  
  755. \item
  756.  
  757. \begin{figure}[ht]
  758. \begin{center}
  759. \includegraphics[width=1\textwidth]{5.Lin.Hetero.Resid.eps}
  760. \end{center}
  761. \caption{Residuals for the heterogeneous variance model with $\text{No. Hornets}$ as the predictor}
  762. \label{5.Lin.Hetero.Resid}
  763. \end{figure}
  764.  
  765. \begin{figure}[ht]
  766. \begin{center}
  767. \includegraphics[width=1\textwidth]{5.log.Hetero.Resid.eps}
  768. \end{center}
  769. \caption{Residuals for the heterogeneous variance model with $\log(\text{No. Hornets})$ as the predictor}
  770. \label{5.log.Hetero.Resid}
  771. \end{figure}
  772.  
  773. \item
  774.  
  775. \begin{figure}[ht]
  776. \begin{center}
  777. \includegraphics[width=1\textwidth]{5.Poisson.Resid.eps}
  778. \end{center}
  779. \caption{Residuals for the Poisson model, both for No. Hornets ans $\log(\text{No. Hornets})$ as the predictor}
  780. \label{5.Poisson.Resid}
  781. \end{figure}
  782.  
  783. \begin{figure}[ht]
  784. \begin{center}
  785. \includegraphics[width=1\textwidth]{5.NB.Resid.eps}
  786. \end{center}
  787. \caption{Residuals for the Negative Binomial model, both for No. Hornets ans $\log(\text{No. Hornets})$ as the predictor}
  788. \label{5.NB.Resid}
  789. \end{figure}
  790.  
  791.  
  792. \begin{figure}[ht]
  793. \begin{center}
  794. \includegraphics[width=0.8\textwidth]{5.Overdisp.eps}
  795. \end{center}
  796. \caption{Within-cell variance vs. within-cell mean. Dashed line: no overdispersion. Solid line: de-facto estimates.}
  797. \label{5.Overdisp.Resid}
  798. \end{figure}
  799.  
  800.  
  801. \begin{figure}[ht]
  802. \begin{center}
  803. \includegraphics[width=1\textwidth]{5.Quasi.Resid.eps}
  804. \end{center}
  805. \caption{Residuals for the Quasi-Likelihood model, both for No. Hornets ans $\log(\text{No. Hornets})$ as the predictor}
  806. \label{5.Quasi.Resid}
  807. \end{figure}
  808.  
  809.  
  810.  
  811. \begin{figure}[ht]
  812. \begin{center}
  813. \includegraphics[width=1\textwidth]{5.Curve.eps}
  814. \end{center}
  815. \caption{$\lambda$ estimates according to the heterogeneous-variance linear model, Poisson model and Quasi-Likelihood model, all in the log scale.}
  816. \label{5.Curve}
  817. \end{figure}
  818.  
  819. \end{enumerate}
  820.  
  821.  
  822.  
  823.  
  824. \end{enumerate}
  825.  
  826.  
  827.  
  828.  
  829. \end{document}
  830.  
  831.  

harario
Posts: 7
Joined: Tue Feb 09, 2010 2:17 pm

Postby harario » Sun Jun 20, 2010 1:40 pm

There we go.
I will appreciate any kind of help.
At the moment the file is not even compiled, and no warnings/errors are to be found.

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  69. LaTeX Font Info: Redeclaring font encoding OMS on input line 568.
  70. \macc@depth=\count92
  71. \c@MaxMatrixCols=\count93
  72. \dotsspace@=\muskip10
  73. \c@parentequation=\count94
  74. \dspbrk@lvl=\count95
  75. \tag@help=\toks17
  76. \row@=\count96
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  78. \maxfields@=\count98
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  83. \tagwidth@=\dimen109
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  86. \@envbody=\toks19
  87. \multlinegap=\skip44
  88. \multlinetaggap=\skip45
  89. \mathdisplay@stack=\toks20
  90. LaTeX Info: Redefining \[ on input line 2666.
  91. LaTeX Info: Redefining \] on input line 2667.
  92. )
  93. ("C:\Program Files\MiKTeX 2.8\tex\latex\amsfonts\amssymb.sty"
  94. Package: amssymb 2009/06/22 v3.00
  95.  
  96. ("C:\Program Files\MiKTeX 2.8\tex\latex\amsfonts\amsfonts.sty"
  97. Package: amsfonts 2009/06/22 v3.00 Basic AMSFonts support
  98. \symAMSa=\mathgroup4
  99. \symAMSb=\mathgroup5
  100. LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
  101. (Font) U/euf/m/n --> U/euf/b/n on input line 96.
  102. ))
  103. ("C:\Program Files\MiKTeX 2.8\tex\latex\ams\classes\amsthm.sty"
  104. Package: amsthm 2004/08/06 v2.20
  105. \thm@style=\toks21
  106. \thm@bodyfont=\toks22
  107. \thm@headfont=\toks23
  108. \thm@notefont=\toks24
  109. \thm@headpunct=\toks25
  110. \thm@preskip=\skip46
  111. \thm@postskip=\skip47
  112. \thm@headsep=\skip48
  113. \dth@everypar=\toks26
  114. )
  115. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\ifpdf.sty"
  116. Package: ifpdf 2010/01/28 v2.1 Provides the ifpdf switch (HO)
  117. Package ifpdf Info: pdfTeX in pdf mode not detected.
  118. )
  119. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\color.sty"
  120. Package: color 2005/11/14 v1.0j Standard LaTeX Color (DPC)
  121.  
  122. ("C:\Program Files\MiKTeX 2.8\tex\latex\00miktex\color.cfg"
  123. File: color.cfg 2007/01/18 v1.5 color configuration of teTeX/TeXLive
  124. )
  125. Package color Info: Driver file: dvips.def on input line 130.
  126.  
  127. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\dvips.def"
  128. File: dvips.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR)
  129. )
  130. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\dvipsnam.def"
  131. File: dvipsnam.def 1999/02/16 v3.0i Driver-dependant file (DPC,SPQR)
  132. ))
  133. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\graphicx.sty"
  134. Package: graphicx 1999/02/16 v1.0f Enhanced LaTeX Graphics (DPC,SPQR)
  135.  
  136. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\keyval.sty"
  137. Package: keyval 1999/03/16 v1.13 key=value parser (DPC)
  138. \KV@toks@=\toks27
  139. )
  140. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\graphics.sty"
  141. Package: graphics 2009/02/05 v1.0o Standard LaTeX Graphics (DPC,SPQR)
  142.  
  143. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\trig.sty"
  144. Package: trig 1999/03/16 v1.09 sin cos tan (DPC)
  145. )
  146. ("C:\Program Files\MiKTeX 2.8\tex\latex\00miktex\graphics.cfg"
  147. File: graphics.cfg 2007/01/18 v1.5 graphics configuration of teTeX/TeXLive
  148. )
  149. Package graphics Info: Driver file: dvips.def on input line 91.
  150. )
  151. \Gin@req@height=\dimen112
  152. \Gin@req@width=\dimen113
  153. )
  154. ("C:\Program Files\MiKTeX 2.8\tex\latex\graphics\epsfig.sty"
  155. Package: epsfig 1999/02/16 v1.7a (e)psfig emulation (SPQR)
  156. \epsfxsize=\dimen114
  157. \epsfysize=\dimen115
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  159. ("C:\Program Files\MiKTeX 2.8\tex\latex\hyperref\hyperref.sty"
  160. Package: hyperref 2010/01/25 v6.80d Hypertext links for LaTeX
  161.  
  162. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\kvsetkeys.sty"
  163. Package: kvsetkeys 2010/01/28 v1.8 Key value parser (HO)
  164.  
  165. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\infwarerr.sty"
  166. Package: infwarerr 2007/09/09 v1.2 Providing info/warning/message (HO)
  167. )
  168. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\etexcmds.sty"
  169. Package: etexcmds 2010/01/28 v1.3 Prefix for e-TeX command names (HO)
  170. Package etexcmds Info: Could not find \expanded.
  171. (etexcmds) That can mean that you are not using pdfTeX 1.50 or
  172. (etexcmds) that some package has redefined \expanded.
  173. (etexcmds) In the latter case, load this package earlier.
  174. ))
  175. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\pdfescape.sty"
  176. Package: pdfescape 2007/11/11 v1.8 Provides hex, PDF name and string conversion
  177. s (HO)
  178.  
  179. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\pdftexcmds.sty"
  180. Package: pdftexcmds 2009/12/12 v0.7 Utility functions of pdfTeX for LuaTeX (HO)
  181.  
  182.  
  183. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\ifluatex.sty"
  184. Package: ifluatex 2009/04/17 v1.2 Provides the ifluatex switch (HO)
  185. Package ifluatex Info: LuaTeX not detected.
  186. )
  187. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\ltxcmds.sty"
  188. Package: ltxcmds 2010/01/28 v1.2 LaTeX kernel commands for general use (HO)
  189. )
  190. Package pdftexcmds Info: LuaTeX not detected.
  191. Package pdftexcmds Info: \pdf@primitive is available.
  192. Package pdftexcmds Info: \pdf@ifprimitive is available.
  193. ))
  194. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\ifvtex.sty"
  195. Package: ifvtex 2008/11/04 v1.4 Switches for detecting VTeX and its modes (HO)
  196. Package ifvtex Info: VTeX not detected.
  197. )
  198. ("C:\Program Files\MiKTeX 2.8\tex\latex\ifxetex\ifxetex.sty"
  199. Package: ifxetex 2009/01/23 v0.5 Provides ifxetex conditional
  200. )
  201. ("C:\Program Files\MiKTeX 2.8\tex\latex\oberdiek\hycolor.sty"
  202. Package: hycolor 2009/12/12 v1.6 Color options of hyperref/bookmark (HO)
  203.  
  204. ("C:\Program Files\MiKTeX 2.8\tex\latex\oberdiek\xcolor-patch.sty"
  205. Package: xcolor-patch 2009/12/12 xcolor patch
  206. ))
  207. \@linkdim=\dimen116
  208. \Hy@linkcounter=\count99
  209. \Hy@pagecounter=\count100
  210.  
  211. ("C:\Program Files\MiKTeX 2.8\tex\latex\hyperref\pd1enc.def"
  212. File: pd1enc.def 2010/01/25 v6.80d Hyperref: PDFDocEncoding definition (HO)
  213. )
  214. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\intcalc.sty"
  215. Package: intcalc 2007/09/27 v1.1 Expandable integer calculations (HO)
  216. )
  217. ("C:\Program Files\MiKTeX 2.8\tex\latex\00miktex\hyperref.cfg"
  218. File: hyperref.cfg 2002/06/06 v1.2 hyperref configuration of TeXLive
  219. )
  220. ("C:\Program Files\MiKTeX 2.8\tex\latex\oberdiek\kvoptions.sty"
  221. Package: kvoptions 2009/12/08 v3.6 Keyval support for LaTeX options (HO)
  222. )
  223. Package hyperref Info: Option `bookmarks' set `false' on input line 3214.
  224. Package hyperref Info: Option `colorlinks' set `true' on input line 3214.
  225. Package hyperref Info: Hyper figures OFF on input line 3295.
  226. Package hyperref Info: Link nesting OFF on input line 3300.
  227. Package hyperref Info: Hyper index ON on input line 3303.
  228. Package hyperref Info: Plain pages OFF on input line 3310.
  229. Package hyperref Info: Backreferencing OFF on input line 3315.
  230.  
  231. Implicit mode ON; LaTeX internals redefined
  232. Package hyperref Info: Bookmarks OFF on input line 3517.
  233. ("C:\Program Files\MiKTeX 2.8\tex\latex\ltxmisc\url.sty"
  234. \Urlmuskip=\muskip11
  235. Package: url 2006/04/12 ver 3.3 Verb mode for urls, etc.
  236. )
  237. LaTeX Info: Redefining \url on input line 3748.
  238.  
  239. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\bitset.sty"
  240. Package: bitset 2007/09/28 v1.0 Data type bit set (HO)
  241.  
  242. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\bigintcalc.sty"
  243. Package: bigintcalc 2007/11/11 v1.1 Expandable big integer calculations (HO)
  244. ))
  245. \Fld@menulength=\count101
  246. \Field@Width=\dimen117
  247. \Fld@charsize=\dimen118
  248. \Field@toks=\toks28
  249. Package hyperref Info: Hyper figures OFF on input line 4707.
  250. Package hyperref Info: Link nesting OFF on input line 4712.
  251. Package hyperref Info: Hyper index ON on input line 4715.
  252. Package hyperref Info: backreferencing OFF on input line 4722.
  253. Package hyperref Info: Link coloring ON on input line 4725.
  254. Package hyperref Info: Link coloring with OCG OFF on input line 4732.
  255. Package hyperref Info: PDF/A mode OFF on input line 4737.
  256.  
  257. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\atbegshi.sty"
  258. Package: atbegshi 2009/12/02 v1.10 At begin shipout hook (HO)
  259. )
  260. \Hy@abspage=\count102
  261. \c@Item=\count103
  262. \c@Hfootnote=\count104
  263. )
  264. *hyperref using default driver hdvips*
  265. ("C:\Program Files\MiKTeX 2.8\tex\latex\hyperref\hdvips.def"
  266. File: hdvips.def 2010/01/25 v6.80d Hyperref driver for dvips
  267.  
  268. ("C:\Program Files\MiKTeX 2.8\tex\latex\hyperref\pdfmark.def"
  269. File: pdfmark.def 2010/01/25 v6.80d Hyperref definitions for pdfmark specials
  270. \pdf@docset=\toks29
  271. \pdf@box=\box28
  272. \pdf@toks=\toks30
  273. \pdf@defaulttoks=\toks31
  274. \Fld@listcount=\count105
  275. \c@bookmark@seq@number=\count106
  276.  
  277. ("C:\Program Files\MiKTeX 2.8\tex\latex\oberdiek\rerunfilecheck.sty"
  278. Package: rerunfilecheck 2010/01/25 v1.3 Rerun checks for auxiliary files (HO)
  279.  
  280. ("C:\Program Files\MiKTeX 2.8\tex\latex\oberdiek\atveryend.sty"
  281. Package: atveryend 2010/01/25 v1.4 Hooks at very end of document (HO)
  282. Package atveryend Info: \enddocument detected (standard).
  283. )
  284. ("C:\Program Files\MiKTeX 2.8\tex\generic\oberdiek\uniquecounter.sty"
  285. Package: uniquecounter 2009/12/18 v1.1 Provides unlimited unique counter (HO)
  286. )
  287. Package uniquecounter Info: New unique counter `rerunfilecheck' on input line 2
  288. 70.
  289. )
  290. \Hy@SectionHShift=\skip49
  291. ))


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