Related
I am sorry for maybe a trivial question, but unfortunately i haven´t found a solution for it. Here is my problem...
I have created a function bm6, with 3 unknown parameters (a, l, p), with which i want to aproximate the measured data, that are found in the dataframe zz. For fitting i have used nls model in r.
nls(zz$tuReMa~bm6(zz$Time, t0=30, tau=10, a, l, p), data=zz, start=list(a=0.01, l=0.01, p=0.1))
The model converges on the whole data range, that means from row 1 till 100, and yield the searched parameters.
Data and fit plot:
https://i.stack.imgur.com/iOn5q.png
Now i want to specify my datarange, so that the nls model will take only the data between row 7 and row 37. How can you do that? I have already tried some things but without a success.
nls(zz$tuReMa[7:37]~bm6(zz$Time[7:37], t0=30, tau=10, a, l, p), data=zz, start=list(a=0.01, l=0.01, p=0.1))
the latter works fine in a lm model
other data argument data=list(zz$Time[7:37],zz$tuReMa[7:37])
with subset argument subset = c(7:37)
One can also create a new dataframe with values from 7:37, and than apply the nls model on the new dataframe, but i hope it goes also without this detour.
Additional data:
bm6 <- function(t, t0=30, tau=10, a, l, p) {
ifelse(t<=(tau+t0), 1+a/(p-l)*(exp(-l*(t-t0))/l*(exp(l*(t-t0))-1)-exp(-p*(t-t0))/p*(exp(p*(t-t0))-1)),
1+a/(p-l)*(exp(-l*(t-t0))/l*(exp(l*tau)-1)-exp(-p*(t-t0))/p*(exp(p*tau)-1)))
}
DATA
structure(list(Time = c(0, 5.01, 10.01, 15.02, 20.02, 25.03,
30.03, 35.04, 40.04, 45.05, 50.05, 55.05, 60.06, 66.07, 71.07,
76.08, 81.08, 86.09, 91.09, 96.1, 101.1, 106.11, 111.11, 116.12,
121.12, 126.13, 131.13, 136.14, 142.14, 147.15, 152.15, 157.16,
162.16, 167.17, 172.17, 177.18, 182.18, 187.19, 192.19, 197.2,
202.2, 207.21, 213.21, 218.22, 223.22, 228.23, 233.23, 238.24,
243.24, 248.25, 253.25, 258.26, 263.26, 268.27, 273.27, 278.28,
284.29, 289.29, 294.29, 299.3, 304.3, 309.31, 314.31, 319.32,
324.32, 329.33, 334.34, 339.34, 344.34, 349.35, 355.36, 360.36,
365.36, 370.37, 375.38, 380.38, 385.39, 390.39, 395.39, 400.4,
405.41, 410.41, 415.41, 420.42, 426.43, 431.43, 436.43, 441.44,
446.45, 451.45, 456.46, 461.46, 466.46, 471.47, 476.48, 481.48,
486.48, 491.49, 497.5, 502.5), tu = c(24.8, 16.4, 24.1, 25.8,
20.2, 21, 18.6, 11.8, 21.1, 66.8, 67.4, 72.5, 73.3, 71.6, 72,
65.5, 67.8, 57.1, 61.5, 58.6, 55.9, 60.2, 54.1, 54.6, 52.7, 54.3,
49.8, 49.4, 54.8, 49, 52.4, 50.8, 45.9, 48.4, 48.1, 48.1, 50.5,
44.2, 42.9, 47.3, 51.7, 46.1, 46.9, 44.6, 46.1, 48, 43.2, 38.5,
49.7, 47, 46.9, 51.8, 45, 46.7, 45.8, 39.8, 43.8, 43.3, 45.5,
45.3, 45.9, 38.9, 44.4, 40.8, 40.5, 39.8, 43, 38, 44.7, 42.1,
43, 39.4, 36.6, 44.9, 42.8, 37.2, 41.7, 41.8, 34.7, 44.4, 43.8,
44.7, 44.6, 46.5, 49.7, 42, 36.3, 43.5, 43.7, 41.7, 39.3, 42.5,
45.4, 37.6, 46, 38.5, 39.6, 37.7, 37.9, 39.9), mu = c(26.64,
27.16, 23.43, 24.35, 24.79, 25.4, 25.27, 23.61, 25.36, 27.47,
30.17, 29.94, 28.06, 32.19, 30.96, 35.87, 32.48, 32.41, 33.09,
35.4, 33.68, 33.5, 32.83, 34.19, 32.25, 34.76, 33.69, 33.03,
35.09, 37.13, 36.64, 33.51, 32.91, 33.56, 34.78, 36.06, 33.74,
32.87, 35.57, 36.17, 35.52, 34.43, 33.85, 33.93, 36.69, 34.77,
34.14, 33.46, 34.14, 34.5, 33.03, 33.69, 33.02, 34.23, 33.22,
35.46, 34.28, 31.87, 32.91, 34.25, 33.75, 33.66, 31.08, 32.72,
36.13, 35.3, 32.37, 31.25, 32.98, 34, 34.3, 33.69, 32.33, 33.01,
36.03, 31.59, 34.09, 30.76, 31.8, 32.93, 35.32, 33.69, 31.58,
33.99, 33.67, 33.89, 32.99, 31.17, 32.08, 33.42, 33.91, 34.36,
31.96, 33.27, 31.9, 33.7, 33.16, 30.01, 32.04, 33.59), tuRE = c(1.15043074884029,
0.76076872100729, 1.11795891318754, 1.19681908548708, 0.937044400265076,
0.974155069582505, 0.862823061630219, 0.547382372432074, 0.978793903247184,
3.0987408880053, 3.12657388999337, 3.36315440689198, 3.40026507620941,
3.32140490390987, 3.33996023856859, 3.03843605036448, 3.14512922465209,
2.64877402253148, 2.85288270377734, 2.71835652750166, 2.59310801855533,
2.79257786613651, 2.50960901259112, 2.53280318091451, 2.44466534128562,
2.51888667992048, 2.31013916500994, 2.29158383035123, 2.54208084824387,
2.27302849569251, 2.43074884029158, 2.35652750165673, 2.12922465208747,
2.24519549370444, 2.2312789927104, 2.2312789927104, 2.34261100066269,
2.05036447978794, 1.99005964214712, 2.19416832339298, 2.39827700463883,
2.13850231941683, 2.17561298873426, 2.06891981444665, 2.13850231941683,
2.22664015904573, 2.00397614314115, 1.78595096090126, 2.30550033134526,
2.18025182239894, 2.17561298873426, 2.40291583830351, 2.08747514910537,
2.1663353214049, 2.1245858184228, 1.84625579854208, 2.03180914512922,
2.00861497680583, 2.11066931742876, 2.1013916500994, 2.12922465208747,
1.80450629555997, 2.0596421471173, 1.89264413518887, 1.87872763419483,
1.84625579854208, 1.9946984758118, 1.76275679257787, 2.07355864811133,
1.95294897282969, 1.9946984758118, 1.82770046388337, 1.69781312127237,
2.08283631544069, 1.98542080848244, 1.72564612326044, 1.93439363817097,
1.93903247183565, 1.60967528164347, 2.0596421471173, 2.03180914512922,
2.07355864811133, 2.06891981444665, 2.15705765407555, 2.30550033134526,
1.94831013916501, 1.68389662027833, 2.01789264413519, 2.02717031146455,
1.93439363817097, 1.82306163021869, 1.9715043074884, 2.10603048376408,
1.74420145791915, 2.13386348575215, 1.78595096090126, 1.83697813121272,
1.74884029158383, 1.75811795891319, 1.85089463220676), tuMA = c(24.8,
20.6, 21.7666666666667, 22.775, 22.2733333333333, 21.8533333333333,
20.8866666666667, 17.5066666666667, 18.0466666666667, 34.1333333333333,
47.3133333333333, 59.1, 67.56, 71.3533333333333, 71.9133333333333,
69.96, 68.9, 64.5866666666667, 62.82, 60.76, 58.6933333333333,
58.7, 57.18, 56.0266666666667, 54.7, 54.3, 52.5066666666667,
51.2733333333333, 52.1533333333333, 51.0866666666667, 51.4, 51.3066666666667,
49.5133333333333, 48.7866666666667, 48.3866666666667, 48.0466666666667,
48.7933333333333, 47.46, 45.8066666666667, 45.9866666666667,
47.6866666666667, 47.28, 47.4333333333333, 46.64, 46.2333333333333,
46.54, 45.4933333333333, 43.0733333333333, 44.9466666666667,
45.58, 46.12, 48.3666666666667, 47.7733333333333, 47.3133333333333,
46.7533333333333, 44.2733333333333, 43.6, 43.2933333333333, 43.8333333333333,
44.3866666666667, 45.1733333333333, 43.22, 43.4266666666667,
42.36, 41.5066666666667, 40.74, 41.4466666666667, 40.2133333333333,
41.64, 41.94, 42.4333333333333, 41.5133333333333, 39.9, 41.1466666666667,
41.68, 40.3, 40.8066666666667, 41.1933333333333, 38.8666666666667,
40.4533333333333, 41.7333333333333, 42.8733333333333, 43.78,
45.1333333333333, 46.7666666666667, 45.48, 42.4133333333333,
42.3066666666667, 42.34, 41.8933333333333, 41.18, 41.7133333333333,
42.8, 41.16, 42.7266666666667, 41.5066666666667, 40.7066666666667,
39.4666666666667, 38.8066666666667, 38.7933333333333), tuReMa = c(1.15043074884029,
0.955599734923791, 1.00971946101171, 1.05649436713055, 1.03322288491275,
1.0137397835211, 0.968897724762536, 0.812105146896399, 0.837154848685664,
1.58338855754363, 2.19478683454827, 2.74155069582505, 3.13399602385686,
3.309962447537, 3.3359399160592, 3.24532803180915, 3.19615639496355,
2.99606803622708, 2.91411530815109, 2.81855533465871, 2.72268610558869,
2.72299536116634, 2.65248508946322, 2.59898387453059, 2.53744201457919,
2.51888667992048, 2.43569692953391, 2.37848464766954, 2.41930638391871,
2.36982549149547, 2.3843605036448, 2.38003092555776, 2.2968411751712,
2.26313231720786, 2.24457698254915, 2.22880494808924, 2.26344157278551,
2.20159045725646, 2.12489507400044, 2.13324497459686, 2.2121051468964,
2.19324055666004, 2.20035343494588, 2.1635520212061, 2.14468743096974,
2.15891318754142, 2.11036006185112, 1.99810028716589, 2.08500110448421,
2.1143803843605, 2.13943008614977, 2.24364921581621, 2.21612546940579,
2.19478683454827, 2.16880936602607, 2.05376629114204, 2.02253147779987,
2.00830572122819, 2.03335542301745, 2.05902363596201, 2.09551579412414,
2.00490390987409, 2.01449083278109, 1.96500994035785, 1.92542522641926,
1.88986083499006, 1.92264192622046, 1.86542964435609, 1.93161033797217,
1.9455268389662, 1.96841175171195, 1.92573448199691, 1.85089463220676,
1.90872542522642, 1.93346587143804, 1.86944996686547, 1.89295339076651,
1.91089021426994, 1.80296001767175, 1.87656284515131, 1.9359399160592,
1.98882261983654, 2.03088137839629, 2.09366026065827, 2.16942787718136,
2.10974155069583, 1.96748398497901, 1.96253589573669, 1.96408217362492,
1.94336204992269, 1.91027170311465, 1.93501214932626, 1.98542080848244,
1.90934393638171, 1.98201899712834, 1.92542522641926, 1.88831455710183,
1.83079301965982, 1.80017671747294, 1.79955820631765)), row.names = c(NA,
-100L), class = "data.frame")
I will be really thankful for a solution.
nls itself has a subset argument, e.g. using the built-in CO2 data.frame this uses only the first 10 rows:
nls(uptake ~ a + b * conc, CO2, start = list(a = 0, b = 1), subset = 1:10)
ADDED
Regarding the change in question to fully present it, the problems are
zz should not be part of the formula
better starting values are needed
c(7:37) is the same as 7:37. The c is superfluous.
Remove zz and use the result of the full optimization to start the subset problem:
fm0 <- nls(tuReMa ~ bm6(Time, t0=30, tau=10, a, l, p), data=zz,
start=list(a=0.01, l=0.01, p=0.1));
fm <- nls(tuReMa~bm6(Time, t0=30, tau=10, a, l, p), data=zz,
start=coef(fm0), subset = 7:37)
fm
giving:
Nonlinear regression model
model: tuReMa ~ bm6(Time, t0 = 30, tau = 10, a, l, p)
data: zz
a l p
0.014206 0.007979 0.049172
residual sum-of-squares: 1.678
Number of iterations to convergence: 23
Achieved convergence tolerance: 9.615e-06
I neeed to draw a histogram of data (weights) overlayed with a line of the expected normal distributioh
I am totally new to R and statistics. I know I probably got something fundamentally wrong about frequencies density and dnorm, but I am stuck.
weights <- c(97.6,95,94.3 ,92.3 ,90.7 ,89.4 ,88.2 ,86.9 ,85.8 ,85.5 ,84.4 ,84.1 ,82.5 ,81.4 ,80.8 ,80 ,79.8 ,79.5 ,78.4 ,78.4 ,78.2 ,78.1 ,78 ,77.4 ,76.5 ,75.4 ,74.8 ,74.1 ,73.5 ,73.2 ,73 ,72.3 ,72.3 ,72.2 ,71.8 ,71.7 ,71.6 ,71.6 ,71.5 ,71.3 ,70.7 ,70.6 ,70.5 ,69.2 ,68.6 ,68.3 ,67.5 ,67 ,66.8 ,66.6 ,65.8 ,65.6 ,64.9 ,64.6 ,64.5 ,64.5 ,64.3 ,64.2 ,63.9 ,63.7 ,62.7 ,62.3 ,62.2 ,59.4 ,57.8 ,57.8 ,57.6 ,56.4 ,53.6 ,53.2 )
hist(weights)
m <- mean(weights)
sd <- sd(weights)
x <- seq(min(weights), max(weights), length.out length(weights))
xn <- dnorm(x, mean = m, sd = sd) * length(weights) #what is the correct factor???
lines(x, xn)
I expected the line to follow the histogram approximately, but it is too low in the histogram
what you need is to plot the histogram with the frequency of the examples and then plot the density of the weights, i.e.
weights = c(97.6,95,94.3 ,92.3 ,90.7 ,89.4 ,88.2 ,86.9 ,85.8 ,85.5 ,84.4 ,84.1 ,82.5 ,81.4 ,80.8 ,80 ,79.8 ,79.5 ,78.4 ,78.4 ,78.2 ,78.1 ,78 ,77.4 ,76.5 ,75.4 ,74.8 ,74.1 ,73.5 ,73.2 ,73 ,72.3 ,72.3 ,72.2 ,71.8 ,71.7 ,71.6 ,71.6 ,71.5 ,71.3 ,70.7 ,70.6 ,70.5 ,69.2 ,68.6 ,68.3 ,67.5 ,67 ,66.8 ,66.6 ,65.8 ,65.6 ,64.9 ,64.6 ,64.5 ,64.5 ,64.3 ,64.2 ,63.9 ,63.7 ,62.7 ,62.3 ,62.2 ,59.4 ,57.8 ,57.8 ,57.6 ,56.4 ,53.6 ,53.2 )
hist(weights, prob = T)
lines(density(weights), col = "red")
Hope this helps.
The problem in your code is that hist plots frequencies and dnorm calculates densities.
You can try making a histogram with densities and then you will see the histogram or the line just adding freq=F to the histogram:
hist(weights, freq = F)
You're nearly there, you just have to factor in the histogram bin widths.
weights <- c(97.6, 95, 94.3, 92.3, 90.7, 89.4, 88.2, 86.9, 85.8,
85.5, 84.4, 84.1, 82.5, 81.4, 80.8, 80, 79.8, 79.5, 78.4, 78.4,
78.2, 78.1, 78, 77.4, 76.5, 75.4, 74.8, 74.1, 73.5, 73.2, 73,
72.3, 72.3, 72.2, 71.8, 71.7, 71.6, 71.6, 71.5, 71.3, 70.7,
70.6, 70.5, 69.2, 68.6, 68.3, 67.5, 67, 66.8, 66.6, 65.8, 65.6,
64.9, 64.6, 64.5, 64.5, 64.3, 64.2, 63.9, 63.7, 62.7, 62.3,
62.2, 59.4, 57.8, 57.8, 57.6, 56.4, 53.6, 53.2)
h <- hist(weights, freq=TRUE)
binwi <- diff(h$breaks)[1]
x <- seq(min(weights)-10, max(weights)+10, 0.01)
xn <- dnorm(x, mean=mean(weights), sd=sd(weights)) * length(weights) * binwi
lines(x, xn)
I am writing a function which returns a plotly object. I managed to control the colors already. However I have trouble controlling the linetype. Currently I use something like:
plot_ly(colors=c(rep(c("#CD0C18","#1660A7"),each=3),'#9467bd'),linetypes = c(rep(c("dot","dash","solid"),2),"dot")) %>%
add_trace(data=long_data,x=~month,y=~temperature,color=~measure,linetype=~measure,type="scatter",mode="lines",line=list(width=4)) %>%
layout(title = "Average High and Low Temperatures in New York",
xaxis = list(title = "Months", categoryorder="array", categoryarray=month),
yaxis = list (title = "Temperature (degrees F)"))
which returns me a warning:
Warning message:
plotly.js only supports 6 different linetypes
The warning makes sense, since measure has seven levels. However I would like to control the linetype without getting a warning every time I have more than 6 traces to plot - is there a way?
My sample data:
month <- c('January', 'February', 'March', 'April', 'May', 'June', 'July',
'August', 'September', 'October', 'November', 'December')
high_2000 <- c(32.5, 37.6, 49.9, 53.0, 69.1, 75.4, 76.5, 76.6, 70.7, 60.6, 45.1, 29.3)
low_2000 <- c(13.8, 22.3, 32.5, 37.2, 49.9, 56.1, 57.7, 58.3, 51.2, 42.8, 31.6, 15.9)
mid_2000 <-apply(rbind(high_2000,low_2000),2,mean)
high_2007 <- c(36.5, 26.6, 43.6, 52.3, 71.5, 81.4, 80.5, 82.2, 76.0, 67.3, 46.1, 35.0)
low_2007 <- c(23.6, 14.0, 27.0, 36.8, 47.6, 57.7, 58.9, 61.2, 53.3, 48.5, 31.0, 23.6)
high_2014 <- c(28.8, 28.5, 37.0, 56.8, 69.7, 79.7, 78.5, 77.8, 74.1, 62.6, 45.3, 39.9)
low_2014 <- c(12.7, 14.3, 18.6, 35.5, 49.9, 58.0, 60.0, 58.6, 51.7, 45.2, 32.2, 29.1)
data <- data.frame(month, high_2000, low_2000,mid_2000, high_2007, low_2007, high_2014, low_2014)
long_data<-tidyr::gather(data,measure,temperature,-month)
As can be seen here, the warning arises in
validLinetypes <- as.character(Schema$traces$scatter$attributes$line$dash$values)
if (length(pal) > length(validLinetypes)) {
warning("plotly.js only supports 6 different linetypes", call. = FALSE)
}
So, if you want to disable this warning alone, there are only two things you can do: override the whole function or manually extend Schema$traces$scatter$attributes$line$dash$values. The latter is somewhat less intrusive and can be done with
tmp <- plotly:::Schema
tmp$traces$scatter$attributes$line$dash$values <- c(tmp$traces$scatter$attributes$line$dash$values, rep(NA, 100))
assignInNamespace("Schema", tmp, ns = "plotly")
Here we add NA 100 times so that up to 106 line types now wouldn't provoke a warning. The last line overrides the Schema variable with tmp in the plotly package environment.
The vector Schema$traces$scatter$attributes$line$dash$values only gets used (through validLinetypes) here four times, and looking at those it seems like this cheating doesn't have any likely side effects.
I have soil moisture data with x-, y- and z-coordinates like this:
gue <- structure(list(x = c(311939.1507, 311935.4607, 311924.7316, 311959.553,
311973.5368, 311953.3743, 311957.9409, 311948.3151, 311946.7169,
311997.0803, 312017.5236, 312006.0245, 312001.5179, 311992.7044,
311977.3076, 311960.4159, 311970.6047, 311957.2564, 311866.4246,
311870.8714, 311861.4461, 311928.7096, 311929.6291, 311929.4233,
311891.2915, 311890.3429, 311900.8905, 311864.4995, 311870.8143,
311866.9257, 312002.571, 312017.816, 312004.5024, 311947.1186,
311943.0152, 311952.2695, 311920.6095, 311929.8371, 311918.6095,
312011.9019, 311999.5755, 312011.1461, 311913.7251, 311925.3459,
311944.4701, 311910.2079, 311908.7618, 311896.0776, 311864.4814,
311856.9027, 311857.5747, 311967.3779, 311962.2024, 311956.8318,
311977.5254, 311971.1776, 311982.537, 311993.4709, 312004.6407,
312015.6118, 311990.8601, 311994.686, 311988.3037, 311990.518,
311986.3918, 311998.8876, 311923.9157, 311903.4563, 311915.714,
311856.9087, 311858.9812, 311874.5867, 311963.9099, 311938.4542,
311945.9505, 311804.3039, 311797.2571, 311791.6967, 311921.3965,
311928.9353, 311920.0597, 311833.5109, 311829.8683, 311847.6261,
311889.1243, 311902.4909, 311901.245, 311981.1118, 312005.7098,
311976.5858, 311819.8901, 311816.4143, 311819.4172, 311870.418,
311873.2656, 311888.3401, 311910.8377, 311897.6697, 311902.4571,
311846.8196, 311833.6235, 311846.2942, 311931.3916, 311930.1891,
311947.659, 311792.2642, 311793.2539, 311794.1931, 311795.1288,
311796.0806, 311797.0142, 311797.95, 311798.8822, 311799.8229,
311800.7774, 311801.7094, 311802.6395, 311803.583, 311804.5185,
311805.4558, 311806.391, 311807.3346, 311808.2757, 311809.2187,
311810.1549, 311811.1014, 311812.0366, 311812.9667, 311813.9107,
311814.8373, 311815.7777, 311816.7365, 311817.6522, 311818.6091,
311819.5335, 311820.4961, 311821.4337, 311822.3855, 311823.3195,
311824.2713, 311825.214, 311826.1705, 311827.1188, 311828.0501,
311828.9893, 311829.9324, 311830.8706, 311831.8181, 311832.7667,
311833.705, 311834.6546, 311835.609, 311836.5527, 311837.5157,
311838.4495, 311839.3926, 311840.3423, 311841.2799, 311842.2288,
311843.1691, 311844.118, 311845.0746, 311846.019, 311846.9709,
311847.9201, 311848.859, 311849.8105, 311850.7503, 311851.6889,
311852.6355, 311853.6045, 311854.5296, 311855.4717, 311856.4171,
311857.3759, 311858.3151, 311859.2604, 311860.2178, 311861.1636,
311862.1071, 311863.0347, 311863.9857, 311864.9316, 311865.8722,
311866.8158, 311867.7702, 311868.7155, 311869.649, 311870.6018,
311871.5449, 311872.4871, 311873.4352, 311874.385, 311875.3042,
311876.2617, 311877.2068, 311878.1429, 311879.0956, 311880.0401,
311880.9822, 311881.929, 311882.8651, 311883.8017, 311884.7429,
311885.6949, 311886.6349, 311887.7207, 311888.6653, 311889.6041,
311890.5358, 311891.4838, 311892.4292, 311893.3736, 311894.326,
311895.2703, 311896.2182, 311897.1635, 311898.1032, 311899.0496,
311899.9967, 311900.9456, 311901.8889, 311902.8162, 311903.7566,
311904.6996, 311905.6627, 311906.5899, 311907.5448, 311908.4856,
311909.4399, 311910.3649, 311911.3188, 311912.2629, 311913.2022,
311914.1527, 311915.1025, 311916.0425, 311916.985, 311917.9254,
311918.8661, 311919.8174, 311920.7668, 311921.7026, 311922.6517,
311923.5949, 311924.5252, 311925.4599, 311926.422, 311927.3646,
311928.3, 311929.2432, 311930.1796, 311931.1358, 311932.0726,
311933.0069, 311933.9585, 311934.845, 311935.7788, 311936.7193,
311937.6441, 311938.572, 311939.5094, 311940.4666, 311941.4067,
311942.3489, 311943.2712, 311944.2195, 311945.1536, 311946.0927,
311947.0413, 311947.9761, 311948.9082, 311949.8557, 311950.8201,
311951.7616, 311952.7148, 311953.7894, 311954.7289, 311955.6646,
311956.6081, 311957.5588, 311958.4896, 311959.4297, 311960.3761,
311961.3191, 311962.2653, 311963.195, 311964.1501, 311965.0856,
311966.0254, 311966.9739, 311967.9305, 311968.8592, 311971.7861,
311970.758, 311969.8205), y = c(5846548.408, 5846546.489, 5846538.014,
5846525.283, 5846510.302, 5846503.516, 5846529.769, 5846523.06,
5846522.742, 5846512.263, 5846525.347, 5846522.042, 5846537.487,
5846545.587, 5846532.112, 5846425.917, 5846406.543, 5846434.03,
5846500.989, 5846498.286, 5846487.134, 5846488.045, 5846483.29,
5846468.713, 5846534.269, 5846533.527, 5846504.056, 5846453.395,
5846438.43, 5846442.608, 5846406.8, 5846434.58, 5846419.229,
5846441.045, 5846436.903, 5846447.917, 5846460.757, 5846457.428,
5846451.067, 5846445.596, 5846474.031, 5846457.239, 5846532.694,
5846553.938, 5846565.323, 5846446.926, 5846432.549, 5846467.236,
5846473.963, 5846464.78, 5846498.142, 5846458.168, 5846474.018,
5846489.801, 5846559.513, 5846589.975, 5846555.723, 5846553.847,
5846560.066, 5846560.792, 5846455.642, 5846546.374, 5846465.999,
5846432.091, 5846422.061, 5846442.871, 5846485.956, 5846472.811,
5846506.756, 5846416.327, 5846419.623, 5846413.124, 5846587.334,
5846600.116, 5846589.515, 5846463.69, 5846456.712, 5846459.683,
5846600.118, 5846574.99, 5846597.804, 5846419.496, 5846437.615,
5846436.902, 5846567.872, 5846572.857, 5846556.904, 5846388.146,
5846393.088, 5846390.13, 5846481.09, 5846496.127, 5846493.586,
5846545.396, 5846532.126, 5846538.334, 5846388.343, 5846416.117,
5846392.223, 5846513.526, 5846486.644, 5846512.917, 5846395.509,
5846386.421, 5846383.873, 5846459.062, 5846459.36, 5846459.682,
5846460.026, 5846460.377, 5846460.703, 5846461.047, 5846461.378,
5846461.73, 5846462.071, 5846462.418, 5846462.765, 5846463.115,
5846463.466, 5846463.815, 5846464.128, 5846464.505, 5846464.843,
5846465.189, 5846465.52, 5846465.869, 5846466.217, 5846466.557,
5846466.893, 5846467.237, 5846467.586, 5846467.903, 5846468.274,
5846468.601, 5846468.943, 5846469.258, 5846469.592, 5846469.909,
5846470.247, 5846470.565, 5846470.891, 5846471.24, 5846471.536,
5846471.885, 5846472.224, 5846472.553, 5846472.884, 5846473.225,
5846473.532, 5846473.89, 5846474.179, 5846474.502, 5846474.827,
5846475.146, 5846475.448, 5846475.768, 5846476.102, 5846476.428,
5846476.746, 5846477.069, 5846477.37, 5846477.685, 5846478.009,
5846478.335, 5846478.656, 5846478.958, 5846479.299, 5846479.608,
5846479.926, 5846480.267, 5846480.603, 5846480.908, 5846481.246,
5846481.56, 5846481.877, 5846482.19, 5846482.503, 5846482.825,
5846483.144, 5846483.468, 5846483.811, 5846484.13, 5846484.458,
5846484.8, 5846485.125, 5846485.456, 5846485.778, 5846486.112,
5846486.421, 5846486.75, 5846487.08, 5846487.401, 5846487.744,
5846488.067, 5846488.39, 5846488.728, 5846489.067, 5846489.383,
5846489.716, 5846490.054, 5846490.38, 5846490.719, 5846491.044,
5846491.357, 5846491.694, 5846492.005, 5846492.402, 5846492.726,
5846493.045, 5846493.389, 5846493.708, 5846494.049, 5846494.363,
5846494.686, 5846494.982, 5846495.3, 5846495.64, 5846495.957,
5846496.263, 5846496.584, 5846496.911, 5846497.241, 5846497.591,
5846497.914, 5846498.226, 5846498.553, 5846498.893, 5846499.221,
5846499.538, 5846499.869, 5846500.19, 5846500.508, 5846500.82,
5846501.151, 5846501.492, 5846501.827, 5846502.147, 5846502.471,
5846502.803, 5846503.129, 5846503.46, 5846503.783, 5846504.11,
5846504.448, 5846504.76, 5846505.118, 5846505.445, 5846505.79,
5846506.106, 5846506.465, 5846506.795, 5846507.118, 5846507.448,
5846507.758, 5846508.081, 5846508.396, 5846508.645, 5846508.99,
5846509.34, 5846509.685, 5846510.031, 5846510.363, 5846510.693,
5846511.031, 5846511.362, 5846511.694, 5846512.024, 5846512.354,
5846512.701, 5846513.034, 5846513.353, 5846513.683, 5846513.998,
5846514.32, 5846514.636, 5846514.956, 5846515.326, 5846515.65,
5846515.968, 5846516.301, 5846516.634, 5846516.971, 5846517.318,
5846517.64, 5846517.952, 5846518.308, 5846518.626, 5846518.937,
5846519.27, 5846519.597, 5846519.921, 5846520.245, 5846520.581,
5846521.498, 5846521.209, 5846520.893), z = c(26.485, 26.411,
26.339, 27.248, 27.208, 26.799, 27.199, 27.023, 26.973, 26.908,
26.275, 26.474, 26.316, 26.226, 27.184, 25.903, 25.765, 25.931,
26.057, 26.181, 26.102, 26.436, 26.457, 26.396, 25.585, 25.572,
26.448, 25.637, 25.603, 25.634, 25.847, 26.185, 25.899, 26.016,
25.873, 26.299, 26.358, 26.344, 26.088, 26.264, 26.3, 26.306,
26.311, 25.857, 26.004, 25.824, 25.798, 26.326, 26.03, 25.625,
25.78, 26.368, 26.225, 26.582, 26.398, 25.343, 26.253, 25.908,
25.323, 25.381, 26.3, 26.179, 26.284, 26.024, 25.896, 26.251,
26.447, 26.385, 26.419, 25.188, 25.176, 25.169, 25.348, 25.188,
25.291, 25.285, 25.266, 25.262, 25.333, 25.308, 25.314, 25.145,
25.172, 25.22, 25.235, 25.204, 25.286, 25.155, 25.397, 25.202,
25.373, 25.327, 25.341, 25.172, 25.253, 25.318, 25.023, 25.24,
25.132, 25.264, 25.38, 25.221, 25.119, 25.179, 25.083, 25.258,
25.254, 25.235, 25.252, 25.266, 25.256, 25.264, 25.26, 25.262,
25.265, 25.265, 25.285, 25.28, 25.257, 25.254, 25.258, 25.287,
25.294, 25.282, 25.27, 25.268, 25.309, 25.303, 25.3, 25.312,
25.305, 25.3, 25.314, 25.319, 25.328, 25.304, 25.325, 25.308,
25.332, 25.333, 25.333, 25.346, 25.344, 25.339, 25.355, 25.362,
25.36, 25.391, 25.418, 25.434, 25.436, 25.447, 25.486, 25.5,
25.526, 25.552, 25.551, 25.564, 25.589, 25.606, 25.641, 25.672,
25.689, 25.709, 25.736, 25.758, 25.782, 25.836, 25.844, 25.866,
25.88, 25.935, 25.984, 26.037, 26.066, 26.071, 26.094, 26.106,
26.106, 26.118, 26.1, 26.146, 26.135, 26.156, 26.169, 26.162,
26.173, 26.198, 26.196, 26.228, 26.258, 26.276, 26.283, 26.277,
26.236, 26.277, 26.251, 26.264, 26.26, 26.261, 26.249, 26.307,
26.289, 26.243, 26.206, 26.231, 26.224, 26.238, 26.244, 26.245,
26.254, 26.2, 26.229, 26.24, 26.248, 26.223, 26.29, 26.344, 26.371,
26.364, 26.311, 26.343, 26.342, 26.334, 26.317, 26.342, 26.315,
26.312, 26.322, 26.325, 26.324, 26.32, 26.308, 26.329, 26.31,
26.32, 26.327, 26.34, 26.371, 26.442, 26.442, 26.483, 26.504,
26.526, 26.562, 26.562, 26.538, 26.534, 26.533, 26.541, 26.584,
26.642, 26.65, 26.691, 26.719, 26.755, 26.786, 26.794, 26.849,
26.867, 26.919, 26.93, 26.945, 26.947, 26.959, 26.984, 26.992,
27.006, 27.035, 27.021, 27.052, 27.094, 27.104, 27.119, 27.16,
27.182, 27.223, 27.236, 27.267, 27.304, 27.331, 27.348, 27.341,
27.379, 27.355, 27.378, 27.357, 27.373, 27.319, 27.299, 27.278,
27.28, 27.295, 27.288, 27.286, 27.279), soil_m_sat = c(24.1,
24.2, 26.9, 13.9, 20.6, 34.1, 16.2, 16.7, 16, 22.1, 23.9, 27.2,
26.8, 34.4, 26.3, 54.1, 51, 44.9, 46.4, 45.9, 54.7, 39.1, 38.7,
40.7, 56.5, 56.3, 40.6, 60.9, 56.8, 56.3, 40.7, 40.4, 44.1, 44.9,
46.2, 45.3, 46.1, 43.7, 44.9, 45.4, 33.1, 45.8, 27.6, 47.8, 37.3,
58.9, 51.4, 42.1, 46, 66.6, 51.1, 31.6, 48.7, 32.9, 28.1, 84,
37.7, 38.2, 80.4, 73.3, 35.6, 44.2, 39.7, 50.2, 49.9, 37.8, 37,
41.7, 27.3, 100, 100, 100, 80.9, 100, 88.4, 89.6, 93.8, 95.3,
91.9, 93.9, 96.1, 91.4, 100, 94.4, 100, 100, 80, 94.1, 84.4,
91.1, 80, 78.9, 85.9, 100, 97.5, 87.2, 88.6, 83.3, 90.7, 100,
82.2, 100, 96.3, 93.3, 99.6, 92.1, 92.8, 90.9, 92.3, 91.2, 94.5,
91.8, 89.4, 87, 86, 88, 83.7, 88.8, 92.9, 89.3, 83.3, 83.5, 84.5,
85.8, 87.4, 86.5, 82, 78.1, 85.8, 85.6, 88.7, 87.7, 84.9, 82,
87.9, 85.5, 86, 82, 83, 88.5, 81.2, 81.6, 76.5, 77.6, 84.5, 81.5,
82, 82.4, 68, 67.7, 62.1, 68.9, 61.7, 68.5, 68.6, 65.3, 59.5,
60.8, 67.3, 66.2, 59.9, 50.9, 46.9, 44.6, 47.9, 53, 52.1, 48.3,
41.3, 53.8, 51, 47, 53.7, 49.5, 51.1, 44.4, 35.1, 42.2, 41.5,
40, 48.2, 46.7, 48.6, 51.7, 51.2, 52.3, 53.4, 48.9, 50.7, 48.5,
46.5, 39.4, 38, 49.2, 43.6, 47.1, 40.4, 44.7, 45.7, 38.1, 41.9,
39.3, 40.2, 43.8, 47.3, 50.1, 41.2, 39.8, 46, 40.8, 40, 37.8,
42.6, 46, 43.8, 45.4, 42.2, 46.5, 40.4, 39.9, 53, 44.7, 35.8,
42.9, 43.9, 43.2, 40.6, 40.8, 32.2, 32.6, 33.5, 36.7, 34.6, 34.7,
50.9, 35.6, 34.2, 28.1, 42, 32, 42.3, 30, 29.6, 31, 29.8, 26,
37.8, 40, 37, 30.2, 28.2, 26.2, 27.4, 22.1, 28.4, 23.2, 24.8,
26.5, 23.9, 21.1, 27.2, 20.8, 12.5, 14, 17.9, 19.7, 19.4, 26,
16.7, 18.2, 23.9, 19, 25.9, 24.4, 22.1, 19.2, 18.4, 24.7, 17.3,
19.4, 19.6, 17.7, 21.3, 22.1, 17.9, 28.2, 16.3, 25.3, 19.7, 21.7,
19, 18.8, 11.8, 15.6, 9.8, 17.7)), .Names = c("x", "y", "z",
"soil_m_sat"), class = "data.frame", row.names = c(NA, -296L))
In order to estimate a variogram for this data I need to remove the spatial trend from it. The soil moisture, of course, varies with the surface - the higher a point is the dryer it is. And since this soil moisture data is percetagewise the relationship is hardly linear, what leads me to allow up to cubic dependencies of the soil moisture to the z-coordinate. It happens that in this area there is a small more or less elliptic elevation, so that I want to allow the soil moisture to be dependend of the x- and y-coordinates in a quadratic way. I hope the following model does exactly this:
polymod <- lm(soil_m_sat ~ poly(x + y, degree = 2) + poly(z, degree = 3), data = gue)
summary(polymod)
The summary shows me that there is no significance for the first coefficient of the x- and y-dependency (what summary names poly(x + y, degree = 2)1). Because the help page from poly() told me that it "returns or evaluates orthogonal polynomials of degree 1 to degree", I thought, removing a degree one polynom from the model might be the same as removing the first coefficient of the degree 2 polynom. Therefore I tried to remove it like this:
mod <- lm(soil_m_sat ~ poly(x + y, degree = 2) - poly(x + y, degree = 1) + poly(z, degree = 3), data = gue)
summary(mod)
But the summary of mod looks exactly the same as the summary of polymod, meaning mod does not differ from polymod. How is it possible to remove the unsignificant component then?
No, don't check with summary in this case. You should use anova. A polynomial term from poly(), or a spline term from bs() contains more than coefficients, so they are more like a factor variable with multiple levels.
> anova(polymod)
Analysis of Variance Table
Response: soil_m_sat
Df Sum Sq Mean Sq F value Pr(>F)
poly(x + y, degree = 2) 2 113484 56742 1600.8 < 2.2e-16 ***
poly(z, degree = 3) 3 68538 22846 644.5 < 2.2e-16 ***
Residuals 290 10280 35
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The ANOVA table clearly shows that you need all model terms. Do not drop any.
But I still need to answer your question and make you feel happy.
It is not impossible to drop the poly(x + y, degree = 2)1 term, but you need to access model matrix for such purpose. You may do
gue$XY_poly <- with(gue, poly(x + y, degree = 2))[, 2] ## use the 2nd column only
fit <- lm(soil_m_sat ~ XY_poly + poly(z, degree = 3), data = gue)
summary(fit)
## ...
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 52.3071 0.3459 151.217 < 2e-16 ***
XY_poly -18.8515 7.3894 -2.551 0.0112 *
poly(z, degree = 3)1 -418.1634 6.4937 -64.395 < 2e-16 ***
poly(z, degree = 3)2 116.5327 6.9171 16.847 < 2e-16 ***
poly(z, degree = 3)3 -28.7773 5.9517 -4.835 2.16e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.951 on 291 degrees of freedom
Multiple R-squared: 0.9464, Adjusted R-squared: 0.9457
F-statistic: 1285 on 4 and 291 DF, p-value: < 2.2e-16
I'm trying to make a 2d density plot where the density is displayed for each category. For example, in the image below, we have a density plot for each day, and all the daily densities are combined into the coloured plots. These types of plots are common in the scientific literature on atmospheric sciences and aerosol pollution studies.
So far I've got this
ggplot(dat, aes(y = `dN/dlogDp`, x = date)) +
stat_density2d(geom="tile", aes(fill = ..density..), contour = FALSE) +
scale_fill_gradient(low="blue", high="red") +
geom_point(alpha = 0.1) +
theme_bw()
But I want to facet it by day, and I'm not sure where to start.
Here are the example data:
structure(list(date = structure(c(1359244800, 1359245400, 1359246000,
1359246600, 1359247200, 1359247800, 1359248400, 1359249000, 1359249600,
1359250200, 1359250800, 1359251400, 1359252000, 1359252600, 1359253200,
1359253800, 1359254400, 1359255000, 1359255600, 1359256200, 1359256800,
1359257400, 1359258000, 1359258600, 1359259200, 1359259800, 1359260400,
1359261000, 1359261600, 1359262200, 1359262800, 1359263400, 1359264000,
1359264600, 1359265200, 1359265800, 1359266400, 1359267000, 1359267600,
1359268200, 1359268800, 1359269400, 1359270000, 1359270600, 1359271200,
1359271800, 1359272400, 1359273000, 1359273600, 1359274200, 1359274800,
1359275400, 1359276000, 1359276600, 1359277200, 1359277800, 1359278400,
1359279000, 1359279600, 1359280200, 1359280800, 1359281400, 1359282000,
1359282600, 1359283200, 1359283800, 1359284400, 1359285000, 1359285600,
1359286200, 1359286800, 1359287400, 1359288000, 1359288600, 1359289200,
1359289800, 1359290400, 1359291000, 1359291600, 1359292200, 1359292800,
1359293400, 1359294000, 1359294600, 1359295200, 1359295800, 1359296400,
1359297000, 1359297600, 1359298200, 1359298800, 1359299400, 1359300000,
1359300600, 1359301200, 1359301800, 1359302400, 1359303000, 1359303600,
1359304200), class = c("POSIXct", "POSIXt"), tzone = "UTC"),
`dN/dlogDp` = c(49.8, 49.275, 47.4, 47.975, 48.625, 51.725,
50.7, 47.55, 45.975, 45.35, 45.4, 47.75, 49.625, 48.225,
47.65, 47.3, 48.75, 50.075, 34.725, 42.025, 48.825, 52.25,
54.05, 49.15, 34.6, 34.375, 42.85, 30.325, 43.15, 36.875,
32.85, 36.85, 35.725, 39.8, 38.65, 40.1, 42.675, 38.5, 37.2,
34.425, 25.2, 14.725, 22.675, 14.875, 37.45, 46.025, 49.275,
35.425, 30, 38.9, 28.6, 41.675, 46.05, 48.6, 62.425, 62.65,
61.7, 49.5, 70.05, 71.875, 59.4, 38.525, 36.85, 25.625, 14.675,
14.7, 14.6, 14.725, 15.6, 15, 14.6, 14.75, 15.05, 14.975,
15.425, 15.1, 15.95, 14.95, 15, 14.6, 14.725, 14.85, 15.175,
28.95, 14.975, 14.725, 16.6, 18.925, 53.225, 60.2, 56.425,
54.55, 41.4, 19.025, 19.825, 31.875, 14.85, 16.375, 16.65,
34.325), Diameter = c(14.6, 15.1, 15.7, 16.3, 16.8, 17.5,
18.1, 18.8, 19.5, 20.2, 20.9, 21.7, 22.5, 23.3, 24.1, 25,
25.9, 26.9, 27.9, 28.9, 30, 31.1, 32.2, 33.4, 34.6, 35.9,
37.2, 38.5, 40, 41.4, 42.9, 44.5, 46.1, 47.8, 49.6, 51.4,
53.3, 55.2, 57.3, 59.4, 61.5, 63.8, 66.1, 68.5, 71, 73.7,
76.4, 79.1, 82, 85.1, 88.2, 91.4, 94.7, 98.2, 101.8, 105.5,
109.4, 113.4, 117.6, 121.9, 126.3, 131, 135.8, 140.7, 145.9,
151.2, 156.8, 162.5, 168.5, 174.7, 181.1, 187.7, 194.6, 201.7,
209.1, 216.7, 224.7, 232.9, 241.4, 250.3, 259.5, 269, 278.8,
289, 299.6, 310.6, 322, 333.8, 346, 358.7, 371.8, 385.4,
399.5, 414.2, 429.4, 445.1, 461.4, 478.3, 495.8, 514)), .Names = c("date",
"dN/dlogDp", "Diameter"), row.names = c(NA, 100L), class = c("tbl_df",
"tbl", "data.frame"))
UPDATE This question is misguided and I now think that using categories isn't relevant to recreating this plot. These other questions are more closely related to the task of recreating this plot:
geom_raster interpolation with log scale
Use R to recreate contour plot made in Igor
And after I asked this question I have been keeping an updated gist of R code that combines details from the answers to these questions, and successfully replicates these plots (example output included in the gist). That gist is here: https://gist.github.com/benmarwick/9a54cbd325149a8ff405
The key steps are to strip away much of the decoration in the panels, and use scale_*_continuous(expand = c(0,0)) to make the density plot fill the entire panel. Here's an example of how to put it together:
# get the day and hour to use as facet panels
dat$day <- as.Date(dat$date)
dat$hour <- as.numeric(format(dat$date, "%H"))
library(ggplot2)
library(viridis)
# theme to suppress many details
squeeze_grid_theme <- theme_bw() + theme(axis.title = element_blank(),
axis.ticks = element_blank(),
axis.text = element_blank(),
strip.text = element_blank(),
strip.background = element_blank(),
panel.margin.y = unit(0, "lines"),
panel.margin.x = unit(-1,"lines"),
panel.border = element_blank(),
panel.grid = element_blank(),
axis.text.x = element_text(margin=margin(0,0,0,0,"pt")),
axis.text.y = element_text(margin=margin(0,0,0,0,"pt")))
p <- ggplot(dat, aes(z = Diameter, y = `dN/dlogDp`, x = date)) +
stat_density2d(geom="tile", aes(fill = ..density..), contour = FALSE) +
scale_fill_viridis() +
geom_point(alpha = 0.1) +
facet_grid(~hour) +
scale_y_continuous(expand = c(0,0)) +
scale_x_datetime(expand = c(0,0)) +
squeeze_grid_theme
p
Then we get a separate density plot for each hour, tightly squeezed together like the example plot in the question.