How to calculate the conditional expectation Weibull model? - r

I would like to calculate the conditional expectation of the Weibull model. In specific, I would like to estimate the remaining tenure of a client looking at random moments (time = t) in his total tenure.
To do so, I have calculated the total tenure for each client (currently active or inactive) and based on the random moment for each client, calculated his/her tenure at that moment.
The example below is a snapshot of my attempt. I use 2 variables STED and TemporalTenure to predict the dependent variable tenure which has either status 0 = active or 1 = inactive. I use the survival package for obtaining the survival object (km_surv).
df = structure(list(ID = c(16008, 21736, 18851, 20387, 30749,
42159), STED = c(2,
5, 1, 3, 2, 2), TemporalTenure = c(84, 98, 255, 392, 108, 278
), tenure = c(152, 166, 273, 460, 160, 289), status = c(0, 0,
1, 0, 1, 1)), row.names = c(NA,
6L), class = "data.frame")
km_surv <- Surv(time = df$tenure, event = df$status)
df <- data.frame(y = km_surv, df[,!(names(df) %in% c("tenure","status", "ID"))])
weibull_fit <- psm(y ~. , dist="weibull", data = df)
quantsurv <- Quantile(weibull_fit, df)
lp <- predict(weibull_fit, df, type="lp")
print(quantsurv(0.5, lp))
The output of these estimations are way too high. I assume this is caused by including the TemporalTenure, but I can't find out how the psm package calculates this and if there are other packages where it's possible to estimate the remaining tenure of client i at time t.
How can I obtain the predicted tenure conditioned over the time that a client is already active (random moment in time: TemporalTenure) where the dependent tenure can either be a client that is still active or one that is inactive?
EDIT
To clarify, whenever I add time conditional variables such as: TemporalTenure, number of received payments and number of complaints until time t, the predicted lifetime explodes in many cases. Therefore, I suspect that the psm is not the right way to go. Similar question is asked here, but the solution given doesn't work for the same reasons.
Below a slightly bigger dataset which already causes problems.
df = structure(list(ID= c(16008, 21736, 18851, 20387, 30749,
42159, 34108, 47511, 47917, 61116, 66600, 131380, 112668, 90799,
113615, 147562, 166247, 191603, 169698, 1020841, 1004077, 1026953,
1125673, 1129788, 22457, 1147883, 1163870, 1220268, 2004623,
1233924, 2009026, 2026688, 2031284, 2042982, 2046137, 2043214,
2033631, 2034252, 2068467, 2070284, 2070697, 2084859, 2090567,
2087133, 2087685, 2095100, 2095720, 2100482, 2105150, 2109353,
28852, 29040, 29592, 29191, 31172, 2126369, 2114207, 2111947,
2102678, 237687, 1093221, 2111607, 2031732, 2105275, 2020226,
1146777, 1028487, 1030165, 1098033, 1142093, 1186763, 2005605,
2007182, 2021092, 2027676, 2027525, 2070471, 2070621, 2072706,
2081862, 2085084, 2085353, 2094429, 2096216, 2109774, 2114526,
2115510, 2117329, 2122045, 2119764, 2122522, 2123080, 2128547,
2130005, 30025, 24166, 61529, 94568, 70809, 159214), STED = c(2,
5, 1, 3, 2, 2, 3, 1, 2, 2, 2, 2, 2, 1, 2, 2, 4, 1, 4, 3, 2, 4,
1, 1, 2, 1, 4, 1, 1, 1, 2, 4, 2, 5, 4, 1, 4, 2, 5, 3, 2, 1, 4,
2, 1, 5, 3, 1, 1, 5, 2, 2, 2, 2, 3, 4, 3, 5, 1, 1, 5, 2, 5, 1,
3, 5, 3, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 3, 5, 2, 2, 1, 2, 1, 2,
3, 1, 1, 3, 5, 1, 2, 2, 2, 2, 1, 2, 1, 3, 1), TemporalTenure = c(84,
98, 255, 392, 108, 278, 120, 67, 209, 95, 224, 198, 204, 216,
204, 190, 36, 160, 184, 95, 140, 256, 142, 216, 56, 79, 194,
172, 155, 158, 78, 24, 140, 87, 134, 111, 15, 126, 41, 116, 66,
60, 0, 118, 22, 116, 110, 52, 66, 0, 325, 323, 53, 191, 60, 7,
45, 73, 42, 161, 30, 17, 30, 12, 87, 85, 251, 120, 7, 6, 38,
119, 156, 54, 11, 141, 50, 25, 33, 3, 48, 58, 13, 113, 25, 18,
23, 2, 102, 5, 90, 0, 101, 83, 44, 125, 226, 213, 216, 186),
tenure = c(152, 166, 273, 460, 160, 289, 188, 72, 233, 163,
266, 266, 216, 232, 247, 258, 65, 228, 252, 99, 208, 324,
201, 284, 124, 84, 262, 180, 223, 226, 146, 92, 208, 155,
202, 179, 80, 185, 64, 184, 120, 65, 6, 186, 45, 120, 170,
96, 123, 12, 393, 391, 64, 259, 73, 42, 69, 141, 47, 229,
37, 19, 37, 17, 155, 99, 319, 188, 75, 11, 49, 187, 180,
55, 52, 209, 115, 93, 88, 6, 53, 126, 31, 123, 26, 26, 24,
9, 114, 6, 111, 4, 168, 84, 112, 193, 294, 278, 284, 210),
status = c(0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1,
0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1,
0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0,
1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 0, 0, 0, 1, 0, 1), TotalValue = c(2579.35, 2472.85,
581.19, 2579.35, 2472.85, 0, 1829.18, 0, 936.79, 2098.2,
850.47, 2579.35, 463.68, 463.68, 2171.31, 3043.03, 561.16,
3043.03, 3043.03, -68.06, 2098.2, 2504.4, 1536.67, 2719.7,
3043.03, 109.91, 2579.35, 265.57, 3560.34, 2266.95, 3123.16,
3544.4, 1379.19, 2288.35, 2472.85, 2560.48, 1414.45, 3741.49,
202.2, 2856.23, 1457.75, 313.68, 191.32, 2266.95, 661.01,
0, 2050.81, 298.76, 1605.44, 373.86, 3043.03, 2579.35, 448.63,
3043.03, 463.68, 977.28, 818.06, 2620.06, 0, 3235.8, 280.99,
0, 0, 194.04, 3212.75, -23.22, 1833.46, 1829.18, 2786.7,
0, 0, 3250.38, 936.79, 0, 1045.21, 3043.03, 1988.36, 2472.85,
1197.94, 0, 313.68, 3212.75, 1419.33, 531.14, 0, 96.28, 0,
142.92, 174.79, 0, 936.79, 156.19, 2472.85, 463.68, 3520.69,
2579.35, 3328.87, 2567.88, 3043.03, 1081.14)), row.names = c(NA,
100L), class = "data.frame")


So here's what I have done: 1) added library call to load pkg:rms, removed the attempt to place a Surv object in a dataframe column, 3) built the Surv object inside formula as Therneau expects formulas to be built, and removed ID from the covariates where it most probably does not belong.
library(survival); library(rms)
#km_surv <- Surv(time = df$tenure, event = df$status)
#df <- data.frame(y = km_surv, df[,!(names(df) %in% c("tenure","status"))])
weibull_fit <- psm(Surv(time = tenure, event = status) ~TemporalTenure +STED , dist="weibull", data = df)
quantsurv <- Quantile(weibull_fit, df)
lp <- predict(weibull_fit, df, type="lp")
Results#
print(quantsurv(0.5, lp))
1 2 3 4 5 6
151.4129 176.0490 268.4644 466.8266 164.8640 301.2630

Related

'termlabels' error in coxph() function of survival package

I am trying to analyse a reoccurring event dataset and I am struggling to fit the model.
A subset of my data:
outdat <- structure(list(yr = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3), jday = c(141, 151, 156, 157, 157, 158, 164, 168, 168, 168, 168, 168, 168, 170, 171, 171, 177, 177, 177, 178, 179, 181, 182, 182, 182, 182, 182, 184, 186, 188, 188, 188, 189, 191, 197, 197, 197, 198, 198, 199, 209, 211, 217, 223, 230, 161, 187, 196, 196, 196, 197, 197, 201, 204, 204, 204, 208, 209, 211, 212, 215, 215, 219, 221, 222, 225, 229, 229, 245, 252, 256, 159, 160, 166, 172, 174, 174, 178, 178, 178, 178, 178, 179, 182, 185, 185, 186, 186, 187, 187, 187, 187, 187, 187, 188, 188, 192, 195, 195, 195, 195, 195, 196, 196, 196, 200, 200, 200, 200, 202, 203, 204, 207, 207, 207, 207, 207, 207, 207, 208, 212, 212, 226), out = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)), row.names = c(NA, -123L), class = c("tbl_df", "tbl", "data.frame"))
The data is showing an occurrence of crop disease in a country and I am trying to first the Cox PH model. The survival package manual recommends defining the term cluster() in the formula.
cm <- coxph(Surv(time =jday, event = out ) ~ cluster(yr), data = outdat)
Error in reformulate(temp[1 - tcl]) :
'termlabels' must be a character vector of length at least one
If I do not define covariate as a grouping variable the model is fitted.
cm <- coxph(Surv(time =jday, event = out ) ~ yr, data = outdat)
Note that I have tried changing the class of outdat$yr to character/factor.

A cluster() term adjusts the standard errors of the hazards, but since it's the only term on the right hand side of the formula, you have no covariates to adjust. You need at least one covariate. And I wouldn't include the cluster term unless you had a specific reason to.
See here for more info

Bootstrapping with glm model

I have a negative binomial regression model where I predict Twitter messages' retweet count based on their use of certain word types (ME words, Moral words, and Emotional words):
M1 <- glm.nb(retweetCount ~ ME_words + Moral_words + Emo_words, data = Tweets)
I now want to sample with bootstrapping (for instance, samples of 1,000 with replacement from the dataframe's original 500,000 messages) from the large dataset, Tweets, to run iterations of the model and analyse the variance of the coefficients. What is the best approach to doing this? I am assuming I need to use the boot package, but I am a bit lost with where to start.
Ideally, I would like to create a for loop that can run a number of iterations, and then store the coefficients of each model iteration in a new dataframe. This would be extremely useful for future analyses.
Here is some reproducible data from the much much large dataframe Tweets:
>dput((head(Tweets, 100)))
structure(list(retweetCount = c(1388, 762, 748, 436, 342, 320,
312, 295, 264, 251, 196, 190, 175, 167, 165, 163, 149, 148, 148,
146, 133, 132, 126, 124, 122, 122, 121, 120, 118, 118, 114, 113,
112, 110, 108, 107, 104, 101, 100, 96, 95, 94, 93, 92, 90, 90,
89, 89, 87, 86, 84, 83, 83, 83, 82, 82, 82, 82, 78, 78, 78, 76,
76, 76, 76, 74, 74, 73, 73, 72, 72, 71, 70, 70, 70, 70, 69, 69,
69, 68, 68, 67, 65, 65, 65, 65, 63, 62, 62, 61, 61, 61, 61, 60,
60, 59, 59, 59, 59, 58), ME_words = c(2, 2, 2, 0, 0, 1, 1, 0,
1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1,
0, 3, 0, 1, 0, 1, 1, 4, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0,
0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 1, 0, 0), Moral_words = c(0, 0, 1, 1, 1, 2, 0,
0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 1,
1, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 1, 0,
0, 5, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0,
1, 1, 2, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1,
1, 1, 0, 0, 2, 2, 1, 0, 0), Emo_words = c(0, 0, 1, 1, 0, 0, 2,
0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 3, 1, 1, 2, 0, 0, 0, 0, 0, 1, 1,
1, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 2, 0, 0,
1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 3, 0, 0, 2, 0, 0, 1, 0,
1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0,
1, 0, 0, 1, 2, 2, 0, 0, 0)), row.names = c(NA, -100L), class = c("tbl_df",
"tbl", "data.frame"))

You can use the boot package, but for simple versions of the bootstrap it's almost simpler to roll your own.
fit initial model
library(MASS)
M1 <- glm.nb(retweetCount ~ ME_words + Moral_words +
Emo_words, data = Tweets)
set up data structure for results
nboot <- 1000
bres <- matrix(NA,nrow=nboot,
ncol=length(coef(M1)),
dimnames=list(rep=seq(nboot),
coef=names(coef(M1))))
bootstrap
set.seed(101)
bootsize <- 200
for (i in seq(nboot)) {
bdat <- Tweets[sample(nrow(Tweets),size=bootsize,replace=TRUE),]
bfit <- update(M1, data=bdat) ## refit with new data
bres[i,] <- coef(bfit)
}
structure output
data.frame(mean_est=colMeans(bres),
t(apply(bres,2,quantile,c(0.025,0.975))))

error with extracting data from a list table

I am trying to extract the median values from the following data
df<-structure(list(n = 26L, time = c(64, 77, 142, 148, 167, 175,
181, 218, 286, 294, 323, 362, 375, 414, 427, 442, 455, 460, 505,
543, 544, 548, 598, 604, 771, 951), n.risk = c(26, 25, 24, 23,
22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7,
6, 5, 4, 3, 2, 1), n.event = c(1, 0, 1, 1, 0, 1, 0, 0, 0, 0,
1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0), n.censor = c(0,
1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0,
0, 1, 0, 1), surv = c(0.961538461538462, 0.961538461538462, 0.921474358974359,
0.881410256410256, 0.881410256410256, 0.839438339438339, 0.839438339438339,
0.839438339438339, 0.839438339438339, 0.839438339438339, 0.786973443223443,
0.734508547008547, 0.682043650793651, 0.629578754578755, 0.577113858363858,
0.524648962148962, 0.524648962148962, 0.4663546330213, 0.408060303893637,
0.349765974765975, 0.349765974765975, 0.27981277981278, 0.209859584859585,
0.209859584859585, 0.104929792429792, 0.104929792429792), type = "right",
std.err = c(0.0392232270276368, 0.0392232270276368, 0.0578796660439579,
0.0729817807835649, 0.0729817807835649, 0.0877911880959172,
0.0877911880959172, 0.0877911880959172, 0.0877911880959172,
0.0877911880959172, 0.108967698764172, 0.128980092013706,
0.148762796526449, 0.168939711260041, 0.190043109889266,
0.212620066567793, 0.212620066567793, 0.24309706208875, 0.277404622263805,
0.317431643449181, 0.317431643449181, 0.388281918537096,
0.483834870173886, 0.483834870173886, 0.856794130229766,
0.856794130229766), upper = c(1, 1, 1, 1, 1, 0.997049673308717,
0.997049673308717, 0.997049673308717, 0.997049673308717,
0.997049673308717, 0.974346771572688, 0.945768634864856,
0.912933812389795, 0.876701615980298, 0.837580372384821,
0.795886882462859, 0.795886882462859, 0.751001648029994,
0.70283210436471, 0.651592180391947, 0.651592180391947, 0.598926755204663,
0.541713673163476, 0.541713673163476, 0.56260462703826, 0.56260462703826
), lower = c(0.890389006776242, 0.890389006776242, 0.822651689473135,
0.763934098528765, 0.763934098528765, 0.706741845048289,
0.706741845048289, 0.706741845048289, 0.706741845048289,
0.706741845048289, 0.635633245173389, 0.570438462156972,
0.509547937949868, 0.45211438075625, 0.397645905392106, 0.345848812876783,
0.345848812876783, 0.289595428067216, 0.236917480831754,
0.187749701094333, 0.187749701094333, 0.130725820922461,
0.0812994900059442, 0.0812994900059442, 0.019570157816371,
0.019570157816371), conf.type = "log", conf.int = 0.95, call = survfit(formula = Surv(as.numeric(as.character(all_clin$new_death))[ind_clin],
all_clin$death_event[ind_clin]) ~ event_rna[ind_gene,
ind_tum])), .Names = c("n", "time", "n.risk", "n.event",
"n.censor", "surv", "type", "std.err", "upper", "lower", "conf.type",
"conf.int", "call"), class = "survfit")
I try to get it like below
x1 <- ifelse (is.na(as.numeric(summary(s)$table[,'median'][1])),'NA',as.numeric(summary(s)$table[,'median'][1]))
x2 <- as.numeric(summary(s)$table[,'median'][2])
if(x1 != 'NA' & x2 != 'NA'){
lines(c(0,x1),c(0.5,0.5),col='blue')
lines(c(x1,x1),c(0,0.5),col='black')
lines(c(x2,x2),c(0,0.5),col='red')
}
I get the following error for both comments
Error in summary(s)$table[, "median"] : incorrect number of dimensions

How to set the ranges of the values taken by ggplot2 stat_smooth() to fits lines?

I would like to make stat_smooth to fit a line using only the data from specified ranges, in other words, I want stat_smooth to fit a line between x(0,99), x(100,199) and x(199,299).
I managed to get fairly close using facet_grid as follows:
ggplot(avtimes3, aes(x=trial, y=ttime, colour=factor(id))) +
facet_grid(. ~ brk, scales = "free") +
geom_vline(xintercept = short_bks, colour="red") +
geom_vline(xintercept = long_bks, colour="green") +
geom_point() +
geom_point(shape=21, fill="white")+
opts(title=titl) +
ylab("Time taken (ms)") +
xlab("Trial No.")+
stat_smooth(method="loess")
But it plots lots of empty space on each grid. I haven't been able to find a way of removing it.
The other partial solution I took from another post included creating a group for the ranges, but that doesn't seem to respect the factors passed to qqplot.
ggplot(avtimes3, aes(x=trial, y=ttime, colour=factor(id))) +
geom_vline(xintercept = short_bks, colour="red") +
geom_vline(xintercept = long_bks, colour="green") +
geom_point() +
geom_point(shape=21, fill="white")+
opts(title=titl) +
ylab("Time taken (ms)") +
xlab("Trial No.")+
stat_smooth(method="loess", aes(group=brk))
Any help on how to get this to work?
Thanks!
The data:
> dput(avtimes3)
structure(list(trial = c(0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5,
6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14,
15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 21, 21, 22, 22,
23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 28, 29, 29, 30, 30,
31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38,
39, 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45, 45, 46, 46,
47, 47, 48, 48, 49, 49, 50, 50, 51, 51, 52, 52, 53, 53, 54, 54,
55, 55, 56, 56, 57, 57, 58, 58, 59, 59, 60, 60, 61, 61, 62, 62,
63, 63, 64, 64, 65, 65, 66, 66, 67, 67, 68, 68, 69, 69, 70, 70,
71, 71, 72, 72, 73, 73, 74, 74, 75, 75, 76, 76, 77, 77, 78, 78,
79, 79, 80, 80, 81, 81, 82, 82, 83, 83, 84, 84, 85, 85, 86, 86,
87, 87, 88, 88, 89, 89, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94,
95, 95, 96, 96, 97, 97, 98, 98, 99, 99, 100, 100, 101, 101, 102,
102, 103, 103, 104, 104, 105, 105, 106, 106, 107, 107, 108, 108,
109, 109, 110, 110, 111, 111, 112, 112, 113, 113, 114, 114, 115,
115, 116, 116, 117, 117, 118, 118, 119, 119, 120, 120, 121, 121,
122, 122, 123, 123, 124, 124, 125, 125, 126, 126, 127, 127, 128,
128, 129, 129, 130, 130, 131, 131, 132, 132, 133, 133, 134, 134,
135, 135, 136, 136, 137, 137, 138, 138, 139, 139, 140, 140, 141,
141, 142, 142, 143, 143, 144, 144, 145, 145, 146, 146, 147, 147,
148, 148, 149, 149, 150, 150, 151, 151, 152, 152, 153, 153, 154,
154, 155, 155, 156, 156, 157, 157, 158, 158, 159, 159, 160, 160,
161, 161, 162, 162, 163, 163, 164, 164, 165, 165, 166, 166, 167,
167, 168, 168, 169, 169, 170, 170, 171, 171, 172, 172, 173, 173,
174, 174, 175, 175, 176, 176, 177, 177, 178, 178, 179, 179, 180,
180, 181, 181, 182, 182, 183, 183, 184, 184, 185, 185, 186, 186,
187, 187, 188, 188, 189, 189, 190, 190, 191, 191, 192, 192, 193,
193, 194, 194, 195, 195, 196, 196, 197, 197, 198, 198, 199, 199,
200, 200, 201, 201, 202, 202, 203, 203, 204, 204, 205, 205, 206,
206, 207, 207, 208, 208, 209, 209, 210, 210, 211, 211, 212, 212,
213, 213, 214, 214, 215, 215, 216, 216, 217, 217, 218, 218, 219,
219, 220, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225,
226, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 231, 232,
232, 233, 233, 234, 234, 235, 235, 236, 236, 237, 237, 238, 238,
239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245,
245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251,
252, 252, 253, 253, 254, 254, 255, 255, 256, 256, 257, 257, 258,
258, 259, 259, 260, 260, 261, 261, 262, 262, 263, 263, 264, 264,
265, 265, 266, 266, 267, 267, 268, 268, 269, 269, 270, 270, 271,
271, 272, 272, 273, 273, 274, 274, 275, 275, 276, 276, 277, 277,
278, 278, 279, 279, 280, 280, 281, 281, 282, 282, 283, 283, 284,
284, 285, 285, 286, 286, 287, 287, 288, 288, 289, 289, 290, 290,
291, 291, 292, 292, 293, 293, 294, 294, 295, 295, 296, 296, 297,
297, 298, 298, 299, 299), id = c(1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5, 2, 1.5,
2), ttime = c(2564, 2050.5, 2204.75, 2060.625, 2266.125, 1880.125,
2224.25, 2067, 2215.375, 2199.25, 2333.375, 2434.625, 2278.875,
2102, 2104.5, 2049, 2336.125, 2159.5, 2110.625, 2082.875, 2197.5,
2136.5, 2107.375, 2025, 2342, 2289.875, 2106.25, 2146.75, 2187.25,
2104.875, 2151.375, 2246.375, 2143.75, 2091.625, 2129.625, 2163.875,
2132.5, 2265.25, 1959, 2054.25, 2205.5, 2033, 1992.875, 1965.625,
1983.875, 1973.75, 1953.625, 1936.375, 2012.25, 2106.75, 2115,
2195.375, 2210.875, 2097.625, 2016.25, 2084.375, 2005.25, 2250.875,
2352.875, 2217.625, 2141.75, 2154.375, 2181.625, 2083.5, 2103.5,
1959.5, 2020.75, 2255.25, 2039.125, 2144.125, 2216.125, 2216.125,
2014.125, 2234.625, 1975.625, 2289, 2035.5, 2058.25, 2039.5,
2222.5, 2013.125, 2156.375, 1896.375, 1990.875, 2014.125, 2030.625,
1928.875, 2021, 2013, 2001.5, 1940.625, 2029.375, 2075.5, 2179.375,
1991, 2292.25, 2020.375, 2065.375, 2007.375, 2192.5, 1954.25,
2128.5, 1949.875, 2240.25, 2119.375, 2011.625, 1984.875, 2182,
1955.375, 2010.5, 1924.5, 2043.25, 2033, 2183.375, 2075.75, 2011.375,
1969.625, 2002.375, 1921.5, 2111.875, 1951, 2103, 1780.375, 1935.75,
1930.75, 2044.375, 1892.25, 2128.75, 1973.875, 1992.625, 1920.625,
2093, 2047.875, 2285.625, 1968, 2208.375, 2021.25, 2079.375,
1988.75, 2147.875, 1989, 2026.25, 1873.25, 2084.75, 2010.25,
2163.25, 1960.125, 1987.125, 2043.75, 2154.875, 2188.25, 2402.625,
2101.625, 2019.625, 2447.5, 1996.125, 2009.875, 2037.625, 2195.5,
2123.875, 1986.625, 2093, 1793.125, 1858.125, 1862.625, 1895.5,
1806, 1951.5, 1784.625, 2041.625, 1868.625, 2095.25, 1946.125,
1930.75, 2010.5, 2179.375, 1903.875, 2049.25, 1958.125, 2053.75,
2016.75, 2057.875, 1898.875, 2196.875, 1939.75, 2265.875, 2090.875,
2187.875, 2082.75, 2089.125, 1904, 2303.25, 1982.125, 2094.375,
2205.625, 2259.25, 2018.5, 1882.25, 1978.125, 1901.625, 1834.5,
2019.375, 1802.125, 1929.875, 1700.75, 2019, 1691.125, 1959.375,
1774.375, 2138.375, 1751.25, 2036.125, 1808.5, 2138, 1848, 2109.75,
1823.125, 2001, 1923, 2057.125, 1827.5, 1877.375, 1823.125, 1860.25,
1742.875, 2047.625, 2018.125, 2016.125, 1799, 2095.25, 1735.25,
1951, 1776.625, 2057.125, 1726.125, 2068.5, 1806, 2107.875, 1774.375,
1956, 1920.75, 1943.25, 1714.125, 1756.125, 1789.25, 1941.125,
1734.125, 2195.375, 1788.375, 2005.375, 1832.5, 1861, 1830.25,
2263.625, 1903.75, 2090.375, 2015.875, 2019.25, 1807.375, 2143.375,
1882.5, 1901.75, 1897.125, 1866.75, 1943.125, 1943.875, 1818.75,
2089.5, 1818, 1992.875, 1910.25, 1855.125, 1825.5, 1850.25, 1881.125,
1953.625, 1840.25, 2119.25, 1745.25, 2045.5, 1767.625, 2019.875,
1759.5, 1876.125, 1667.875, 1948, 1767.125, 2046.25, 1721, 1984.5,
1842.875, 2300.125, 1726.625, 2252.875, 1718.75, 1983.625, 1842.375,
2165.125, 1932, 2154.375, 1746.125, 1936.75, 1920.625, 2056.25,
1854.375, 2022.125, 1973.625, 2064.25, 1883.5, 2077.375, 2117.25,
2089, 1759, 2082.875, 1910.75, 1955.75, 1847.375, 1998.25, 1796.375,
2028.5, 1804.5, 1920.625, 1793.25, 1841.125, 1778.625, 1929.25,
1742.25, 1988.875, 1805.375, 1982.75, 1797.125, 1963.75, 1682.875,
2028.25, 1664.375, 2109.5, 1747.625, 1992, 1767.125, 2064.125,
1740.125, 2083.875, 1952.375, 2007.125, 1763.125, 2050, 1780.25,
2181.25, 1810.5, 1990.25, 1706.875, 2029, 1715.125, 2211.375,
1876.375, 2003.625, 1773.5, 1986.75, 1824, 2198.375, 1777.375,
2075, 1761.25, 1873, 1725.125, 1917.75, 1773.875, 1860.25, 1788,
1908.625, 1955.375, 1943.875, 1828.5, 1860.5, 1836.25, 2134.5,
1829.75, 1949.375, 1762, 2058.75, 1736.75, 1908.625, 1816.375,
2113.625, 1868.125, 2042.625, 1796.375, 2280.5, 1773, 1968.125,
1885.75, 2136.375, 1784.5, 2103.875, 1785.875, 2296.875, 1782.625,
1969.125, 1864.75, 2062.5, 1800.75, 2289.75, 1639.5, 2081.75,
1735.125, 1947.375, 1617.875, 1871.125, 1676.375, 1998, 1685,
1929.625, 1762.625, 2073.625, 1698.75, 1834.5, 1669, 1858.875,
1705.625, 2164.625, 1750.125, 1835.875, 1836.25, 1992, 1741.625,
1874.375, 1810.375, 2140.875, 1819.5, 2277.625, 1779.5, 2054.875,
1703.375, 1978.125, 1754.625, 1964.875, 1749.875, 1959.625, 1932.875,
1952.125, 1709.625, 2038.125, 1680.5, 1893, 1664.5, 1961.125,
1700.25, 1871, 1753, 1889.75, 1724, 1878.875, 1827.375, 1849.25,
1850.75, 1977.125, 1783.625, 1977.25, 1895.125, 2097.5, 1716.375,
1985.5, 1675.375, 1845.25, 1764.5, 2089.375, 1766.75, 1848.125,
1730.125, 1991.5, 1865.375, 2030.875, 1864.625, 1960.875, 1739.25,
2204.375, 1758.125, 2175.375, 1871.5, 1994.25, 1739.25, 2028.875,
1646.125, 1958.375, 1709.25, 1914.5, 1638.375, 1965.375, 1691.5,
2154.375, 1833.75, 1892.375, 1891.625, 1999.25, 1752.75, 1952.5,
1702.625, 1907.75, 1671.25, 1947.375, 1734.875, 2125.375, 1745.25,
2145.25, 1756.125, 2095.25, 1707.5, 1939.375, 1738.25, 2102.875,
1862.375, 2152.875, 1719, 2091.25, 1969.25, 2088.125, 1702.875,
2231.625, 2007.5, 2087, 1732.625, 1866.625, 1675.875, 1971.625,
1663.875, 2016.5, 1834, 1927.75, 1777.25, 1995, 2029.125, 2009.5,
1778.5, 1868, 1711.5, 1820.375, 1706.625, 1911.375, 1850, 2001.625,
1753.375, 2105.625, 1812.125, 2028.125, 1820.5, 2205.75, 1812.625,
2238, 1812.125, 2236.25, 1713.375, 2482, 1844.25, 1951.25, 1995.125,
2108.5, 1873.125, 1977, 1849, 2064.25, 1709.75, 1962, 1844, 1828.5,
1735.75, 1974.125, 1675, 2147, 1789.75, 2099.875, 1790.5, 2083,
1713.5, 2250.125, 1930.25, 2321.75, 1742.5, 2189.875, 1840, 2070,
1823.125, 2027.25, 1782.875, 2344, 1788.875, 2106.25, 1824.75,
2251.625, 1902.5, 1961.375, 1873.5, 2158.75, 1855.125, 1933.75,
1825.75, 2001.875, 1887.75, 2002.75, 1945.375, 2230.875), se = c(259.899705930686,
137.567905310172, 228.087917729734, 172.114158284968, 234.074502600897,
109.939827292024, 271.704918063696, 195.301781134443, 227.085803284951,
169.989784356926, 257.363066052332, 353.735067201228, 231.204411529526,
151.548082893092, 230.22527787241, 188.563933833745, 289.179037319443,
130.584537478874, 250.616449800715, 90.5208021672367, 192.562883977454,
178.968373103821, 225.736567192507, 157.087555204096, 222.259179466547,
189.375330032716, 195.44269803266, 156.734278090568, 222.104443738912,
155.254449844211, 229.124571350234, 234.785535687055, 214.213407443538,
136.267454648675, 218.906693878922, 219.006069509826, 181.324098154185,
198.187568984535, 160.006249877934, 152.706271505603, 280.670689090054,
147.26276321111, 197.418648480474, 131.188242273133, 184.134989060821,
117.833531184585, 177.697770857873, 95.0770246957697, 179.782482660098,
149.204886697071, 143.619164061466, 171.956798717003, 225.56939362264,
150.268680500248, 233.734415064864, 134.100833264163, 177.509833731623,
179.588959004802, 302.633231433458, 256.399655776179, 261.114900132927,
194.266379848099, 233.925960318034, 180.624314136117, 204.312523215923,
147.377552080169, 190.48347791119, 143.664757334567, 184.82012853235,
203.166050796949, 199.973965939498, 181.057847652148, 226.143478278409,
219.701090567226, 192.715458040753, 161.770339856053, 161.292214850651,
121.259130731316, 209.589053694537, 141.678080772675, 203.257616049542,
158.180608516702, 146.132393189483, 151.949173539331, 171.350459324492,
194.983967976491, 127.888265615509, 167.346091336829, 133.506152881217,
141.716391833428, 110.950912167112, 128.343141825231, 135.5180536207,
175.427125437561, 133.723194910767, 194.496120967562, 173.14114158892,
142.659927487414, 199.71273454461, 219.278280469622, 135.405970273523,
223.876480612477, 155.919786783828, 219.316531687487, 142.123178151409,
132.259071725048, 131.867823095163, 192.080526268096, 97.3238220544472,
154.800909004345, 143.230957348114, 172.257049409969, 113.881987789365,
301.963629402852, 147.572228078321, 145.94690050788, 116.268306930258,
103.901556687775, 123.388903182464, 217.304134920557, 106.773123959169,
137.984730004032, 172.231876249516, 166.958479654588, 130.019607037884,
182.871142914114, 142.971994010815, 203.262387603525, 68.1171358501557,
215.99462108878, 142.521168540476, 236.726032125143, 124.067728839073,
132.166282913933, 131.916369611313, 236.530271205249, 124.9966785273,
159.275585240084, 89.4242995898925, 208.220816639794, 86.0348766489497,
106.74431232757, 117.217708011326, 186.83259791283, 92.4279159283446,
153.374745313562, 121.694646774505, 171.894115820093, 107.795731097559,
127.720179284358, 272.201064734981, 364.814039590231, 155.784528103495,
143.156624703255, 489.334059134015, 173.340544006382, 83.3367603462002,
166.637431215627, 219.917679403648, 209.582530411224, 228.411747375843,
189.848059548381, 139.321242034884, 107.117331780889, 112.04876768303,
153.452994198782, 110.70181957467, 212.323287868826, 88.1538706507791,
223.663885064493, 109.954525908928, 174.492810944831, 91.7725132947146,
157.710715054042, 91.0863013065866, 274.394589277923, 98.7716409379303,
171.341946119448, 134.708208136274, 186.973140737227, 120.51344767879,
161.766303826141, 86.3732426945488, 199.796095834514, 104.603801829297,
242.194169263011, 161.9110687891, 212.630332930518, 146.398032529715,
205.110722494322, 115.358911972281, 240.223909687846, 120.004380500404,
183.283731791138, 236.191503528992, 204.437359424767, 129.357340064534,
146.524589598957, 121.586893898385, 142.473924619309, 127.924224222221,
188.175823699539, 152.876518506651, 145.462002586341, 87.0048746581806,
133.546273414338, 98.8791537866877, 174.15909572859, 106.353174695714,
186.087147163058, 126.108053158506, 209.25995773371, 98.74281167327,
160.608886073325, 96.4942633379977, 180.464554295692, 109.188473603477,
150.810548134311, 167.763332448678, 179.1967631145, 107.239551605606,
88.4372128970605, 102.662838856827, 97.9408987239608, 106.765670897264,
250.209122357108, 133.851255063757, 171.96443127868, 79.5145988392787,
134.235367651642, 91.3258979854956, 180.483774498271, 100.323216494773,
155.563886451378, 109.931543227722, 157.58716408932, 101.749692874229,
194.113501177238, 76.3331367615477, 161.404881321123, 150.197697100474,
146.905551533727, 100.562780231342, 141.682925362535, 145.424839448326,
138.486517845601, 108.039251713043, 131.377990315295, 112.028525943172,
96.5617747314418, 125.319448952325, 154.683432486205, 95.5564063038909,
200.194721057489, 93.4435945217373, 122.469812242504, 203.591190300212,
211.888510947216, 101.610414521769, 196.474547379189, 103.015775490941,
119.9206210672, 145.295442547246, 128.463967988804, 150.725085301969,
165.399455593766, 104.018499384896, 215.797110400355, 121.178587217379,
119.188841385065, 143.195265035445, 174.310318264787, 134.187901306872,
127.609721696384, 138.859697626777, 122.751482024804, 115.77236747786,
181.758252907537, 103.840494096887, 162.714583594359, 124.458819566382,
205.661861654721, 129.944493644677, 188.241243156222, 100.24442227091,
158.948217084325, 111.493984062562, 148.115875246376, 115.076216979382,
139.682931772538, 136.821630169147, 191.964509136083, 79.2329155762571,
165.804471495365, 81.7984784175633, 230.305537547407, 124.336946798953,
170.654667750402, 154.3081332918, 162.600182030736, 81.7580134779285,
245.344491771992, 129.797636108235, 219.264496995882, 75.4214202000996,
235.570692870072, 162.076253823845, 207.486811112693, 67.3856173717465,
167.51779622945, 132.19219638736, 189.748047232564, 104.87049837095,
158.695737351611, 122.825187912391, 148.869519810374, 78.1129990782584,
197.096672255738, 78.5845626197847, 133.345550035559, 103.367582649771,
175.46753235489, 104.227215735623, 124.734781135816, 156.960975302325,
160.870483619588, 113.155984312427, 166.304737229581, 79.420431317856,
206.602599036342, 114.308392002262, 208.96263763786, 94.5465564644515,
168.996380984074, 108.669048277656, 137.826236357855, 109.913104882903,
151.036892371178, 120.993718476268, 173.60406898416, 89.1802823939078,
119.126199214471, 112.281523969886, 173.941845526026, 109.368550830274,
183.11822878754, 122.79741592209, 194.953634597709, 113.22401941032,
205.555584244957, 113.743200346218, 159.083199256597, 92.3830220757967,
192.970014093604, 106.811405473787, 128.241393125287, 95.926683312979,
236.008152855544, 137.267595801569, 215.379145553337, 126.974538716007,
158.024523413298, 116.186080737509, 152.477633020153, 99.9564972339753,
192.186456152798, 119.916702860777, 201.098123703686, 97.9207040707648,
159.467074243736, 175.587985423263, 175.71460601742, 74.9249624624531,
183.511385400003, 104.460476121012, 195.090363677963, 99.0178104469811,
190.719121962489, 105.451241271567, 249.549934167207, 101.510511419121,
163.787529777802, 122.226799945838, 260.121464587769, 81.4819080488774,
207.000080874725, 100.300074330552, 318.607292984415, 92.1772361114329,
164.345502513542, 89.5695559726789, 220.035868626328, 121.088220495873,
215.86027536845, 110.382361022946, 266.694209422113, 97.2656409566826,
199.965929017563, 114.208416940259, 155.021887855508, 84.6120875356639,
199.733013760155, 111.110948412579, 199.452800539018, 123.88609940183,
133.35290685942, 111.102500534416, 187.941616836947, 98.1187213641864,
234.046011959798, 123.069956877031, 120.168919427731, 127.988132471614,
232.385450852365, 98.7424047712025, 146.951765653127, 105.750717660517,
145.651300506675, 79.970069735942, 258.883932728549, 87.6153194163473,
115.796841416953, 106.095938726634, 166.706649965912, 101.298698606081,
146.769977649674, 108.152494439895, 195.816006705639, 174.924881837074,
249.006880104317, 86.1696831009276, 159.538333671611, 80.2393601090779,
174.212353742289, 63.3733093603744, 186.199723559331, 107.657764218047,
160.516124857554, 126.626480741589, 168.920145705005, 109.61880989202,
105.320503617021, 129.726085051763, 115.527671391502, 106.433077565201,
190.60022087193, 77.0231296429845, 112.304592197165, 119.858845552353,
206.728492576271, 107.217902289816, 139.122047844433, 119.25886272846,
122.684227359743, 103.792504202237, 210.152362882267, 120.954970591184,
104.686393917398, 214.792876769027, 191.32610530565, 79.7480267333126,
222.855494499398, 91.1213746094421, 140.845628513733, 111.331069979845,
177.763178886566, 99.5254364471716, 140.033980251223, 91.6609508499355,
130.849559200087, 135.593791669404, 217.92957885355, 135.812625320434,
250.986371108359, 85.4232633921898, 196.743119093691, 78.9173250714225,
225.198796106589, 134.913331968554, 156.164833932428, 107.713865336429,
166.808641166629, 97.9876882754738, 152.573043104419, 95.9305459322376,
171.318833924186, 111.86454460322, 182.048554894802, 97.4309279145268,
152.878913044185, 133.997168147049, 205.307168608753, 211.624746856654,
175.627827887756, 100.98775562272, 214.86931244031, 81.6376877034831,
119.379609110721, 92.9686487094286, 209.254282896944, 93.4634071823987,
161.94630255339, 119.06507074465, 223.306623758199, 95.2261288985329,
196.493161458612, 131.601943103327, 154.470748213283, 96.1410329374805,
199.033866240683, 123.609976698023, 240.952161634687, 120.094010793925,
249.304657999003, 98.3497312800454, 210.566280496529, 93.4448724993971,
208.160904238936, 144.170162357839, 238.586686851671, 117.022424209453,
141.61642579013, 106.825030089261, 227.534764808432, 76.6747391583434,
202.614782284018, 145.926106545157, 164.683001768332, 104.052141805374,
186.763888372458, 290.37355482083, 247.792756149166, 121.924889056454,
139.544795675081, 90.5098652870819, 128.81228555815, 97.8303811816291,
158.302258072064, 92.8779921648365, 203.965152617164, 89.5191395137694,
128.750026005545, 119.657761598295, 179.974247909845, 133.466823057803,
238.607474287195, 116.294720660791, 201.864700091069, 112.108435629464,
271.062377507466, 83.4109742479969, 239.645348081583, 130.262886667144,
152.792196650035, 176.884388948181, 162.02645286672, 98.7427099479103,
137.316891063804, 122.648306726416, 125.046669859126, 100.13272442114,
180.137447522718, 217.650850807303, 149.685622937828, 100.501021672135,
139.485974397326, 97.2504131463864, 168.918196600772, 149.435096996274,
196.609242398287, 118.348909102341, 97.2902505760102, 79.5321139091445,
234.000338636812, 162.735625873905, 258.4290279748, 82.6042631207027,
234.984151251283, 134.304026107081, 246.673584201586, 132.418632361268,
137.06069432398, 103.267931251672, 181.858657832316, 108.533312446982,
177.572294130749, 130.488060482833, 183.539693789732, 143.39418697124,
155.657584081672, 144.60809105994, 205.197357091028, 124.319639509842,
153.618817439234, 120.377345697365, 157.628795128211, 158.939875199937,
149.213503553992, 103.583978611559, 143.635257000402), brk = c(0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2)), .Names = c("trial", "id",
"ttime", "se", "brk"), row.names = c(NA, -600L), class = "data.frame")

If you are talking about the space between facets, you can try this (also note that we do not have short_brks and long_brks so I removed those from your example code). grid is required for the unit function.
require(ggplot2)
require(grid)
avtimes3$id <- factor(avtimes3$id)
## create and store plot
p <- ggplot(avtimes3, aes(x=trial, y=ttime, colour=id)) +
facet_grid(. ~ brk, scales = "free") +
geom_point(shape=21, fill="white") +
## remove space between panels
opts(panel.margin = unit(0, "lines")) +
ylab("Time taken (ms)") +
xlab("Trial No.")
## as you had
p + stat_smooth(method="loess")
## only one line per facet
p + stat_smooth(method="loess", aes(colour=NULL))
Edit: Rereading what you wrote and tried, I think you may want this:
## setup plot
p <- ggplot(avtimes3, aes(x=trial, y=ttime, colour=id)) +
geom_point(shape=21, fill="white") +
ylab("Time taken (ms)") +
xlab("Trial No.")
p + stat_smooth(aes(group = brk), method="loess")
The here that differs from what you had before is that the first argument to stat_smooth is mapping, the fifth is method. In R you have two options (maybe more). Either give the arguments in order or explicitly name the arguments. In your second example, you gave the arguments out of order and did not name explicitly like:
p + stat_smooth(method = "loess", mapping = aes(group = brk))
To get separate lines for each id and grouping by brk is a bit trickier (conceptually). We need the interaction of brk and id. Colouring alone does not work, as it would with most geoms.
p + stat_smooth(method = "loess", mapping = aes(group = interaction(brk, id)))

image function in R

I'm trying to do something a little bit complicated for a beginner in programming.
I have a matrix 16x16 and I want to plot the values as a heatmap using image() in R.
How can I plot the "0" (zeros) in blue when the sum (row index + column index) is <= 15? Is that possible?
example matrix:
x <- c(3045, 893, 692, 830, 617, 155, 246, 657, 105, 60, 18, 7, 7, 4, 2, 11234,
2985, 2242, 2471, 1575, 366, 503, 1283, 170, 79, 32, 6, 4, 1, 3, 19475, 4756,
3233, 3251, 1810, 409, 575, 1210, 139, 41, 11, 4, 2, 0, 0, 20830, 4739, 2990,
2531, 1346, 298, 325, 612, 60, 17, 1, 0, 1, 0, 0, 15304, 3196, 1885, 1440, 610,
117, 115, 185, 14, 2, 0, 0, 0, 0, 0, 8026, 1535, 806, 539, 223, 33, 37, 39, 0,
0, 0, 0, 0, 0, 0, 3300, 562, 286, 141, 45, 14, 5, 12, 0, 0, 0, 0, 0, 0, 0, 1067,
160, 65, 40, 14, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 277, 47, 6, 2, 1, 0, 1, 0, 0, 0,
0, 0, 0, 0, 0, 72, 6, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 5, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0)
xmat <- matrix(x, ncol = 12)
xmat <- cbind(xmat, rep(0,16), rep(0,16), rep(0,16), rep(0,16))
xmat <- rbind(xmat, rep(0,16))
dimnames(xmat) = list(0:15, 0:15)
xmat
Thanks!
Vitor

Plot the cases meeting the criteria as blue.
xmat.new <- xmat
xmat.new[!((row(xmat) + col(xmat) <= 15) & xmat==0)] <- NA
image(xmat.new,col="blue")
Plot the cases not meeting the criteria as normal. Notice the add=TRUE
xmat.new <- xmat
xmat.new[((row(xmat) + col(xmat) <= 15) & xmat==0)] <- NA
image(xmat.new,add=TRUE)
Result:
Edited to include #Marek's suggestion to simplify the statements.

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