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
Related
I have a series of x and y values that I've used to build a linear model.
I can use predict() to find a value of y from a known value of x, but I'm struggling to calculate x from a known value of y. I've seen a few posts that talk about using the approx() function, but I can't figure out how to implement it for my use case. The idea is to write a function that takes a numerical value of y as an input and returns the expected value of x that it would correspond to, ideally with a prediction interval, eg "The expected value of x is 38.90, plus or minus 0.7", or something like that.
Here's my data:
> dput(x)
c(4.66, 5.53, 5.62, 5.85, 6.26, 6.91, 7.04, 7.32, 7.43, 7.85,
8.1, 8.3, 8.34, 8.53, 8.69, 8.7, 8.73, 8.76, 8.96, 9.06, 9.42,
9.78, 10.3, 10.82, 10.98, 11.07, 11.09, 11.32, 11.75, 12.1, 12.46,
12.5, 12.99, 13.02, 13.28, 13.43, 13.96, 14, 14.07, 14.29, 14.57,
14.66, 15.21, 15.56, 15.97, 16.44, 16.8, 17.95, 18.33, 18.62,
18.92, 19.49, 19.9, 19.92, 20.14, 20.18, 21.19, 22.7, 23.25,
23.48, 23.49, 23.58, 23.7, 23.83, 23.83, 23.97, 24.05, 24.14,
24.15, 24.19, 24.32, 24.62, 24.9, 24.92, 25, 25.06, 25.31, 25.36,
25.86, 25.9, 25.95, 25.99, 26.08, 26.2, 26.27, 26.39, 26.5, 26.51,
26.68, 26.78, 26.82, 26.92, 26.92, 27.05, 27.05, 27.07, 27.32,
27.6, 27.77, 27.8, 27.91, 27.96, 27.97, 28.04, 28.05, 28.15,
28.2, 28.28, 28.37, 28.51, 28.53, 28.53, 28.66, 28.68, 28.72,
28.74, 28.82, 28.83, 28.83, 28.86, 28.89, 28.91, 29.04, 29.2,
29.35, 29.4, 29.42, 29.48, 29.53, 29.65, 29.67, 29.69, 29.7,
29.72, 29.93, 29.97, 30.03, 30.08, 30.09, 30.11, 30.18, 30.62,
30.66, 30.78, 31, 31.32, 31.43, 31.47, 31.69, 31.96, 32.33, 32.5,
32.5, 32.58, 32.7, 32.92, 33.2, 33.6, 33.72, 33.77, 33.95, 34.02,
34.08, 34.42, 34.79, 34.91, 34.99, 35.08, 35.15, 35.49, 35.6,
35.6, 35.74, 35.8, 36.05, 36.17, 36.3, 36.37, 36.84, 37.31, 37.95,
38.75, 38.78, 38.81, 38.9, 39.21, 39.31, 39.5, 42.68, 43.92,
43.95, 44.64, 45.7, 45.95, 46.25, 46.8, 49.08, 50.33, 51.23,
52.76, 53.06, 62)
> dput(y)
c(11.91, 13.491, 13.708, 13.984, 14.624, 15.688, 15.823, 16.105,
16.387, 17.004, 17.239, 17.498, 17.686, 17.844, 17.997, 18.044,
18.003, 18.191, 18.332, 18.25, 18.778, 19.237, 19.693, 20.177,
20.441, 20.876, 20.512, 20.894, 21.493, 21.539, 21.951, 21.763,
22.498, 22.451, 22.744, 22.785, 23.409, 23.314, 23.408, 23.567,
23.849, 23.978, 24.472, 24.678, 25.236, 25.547, 25.676, 26.81,
26.83, 27.275, 27.331, 27.844, 28.009, 28.244, 28.497, 28.555,
29.067, 30.412, 30.788, 30.965, 31.058, 31.423, 31.346, 31.118,
31.252, 31.258, 31.399, 31.605, 31.552, 31.881, 31.822, 31.91,
32.333, 32.174, 32.222, 32.704, 32.445, 32.557, 32.993, 32.845,
32.997, 32.909, 32.911, 33.121, 33.191, 33.156, 33.426, 33.332,
33.52, 33.526, 33.697, 33.379, 33.849, 33.726, 33.538, 33.885,
33.961, 34.284, 34.208, 33.896, 34.278, 34.355, 34.276, 34.267,
34.399, 34.507, 34.492, 34.531, 34.695, 34.642, 34.872, 34.772,
34.813, 34.942, 34.883, 34.948, 34.719, 34.983, 34.99, 35.136,
35.007, 34.026, 35.148, 35.201, 35.459, 35.418, 35.236, 35.411,
35.459, 35.5, 35.665, 35.724, 35.636, 35.667, 35.747, 35.788,
35.882, 35.9, 35.83, 36.106, 36.029, 36.364, 36.358, 36.517,
37.005, 36.74, 36.963, 36.634, 37.04, 37.48, 37.581, 37.78, 37.686,
38.262, 37.998, 37.986, 38.498, 39.296, 38.467, 38.779, 38.885,
38.72, 39.038, 38.932, 39.719, 39.654, 39.367, 40.072, 39.707,
39.742, 39.919, 40.054, 40.189, 40.197, 40.154, 40.383, 42.146,
40.595, 40.971, 41.441, 41.964, 42.328, 42.463, 42.627, 42.633,
42.721, 42.786, 42.857, 45.318, 45.665, 46.406, 46.335, 47.663,
47.181, 48.074, 48.109, 49.931, 50.377, 51.053, 52.451, 53.004,
65.889)
> model <- lm(y ~ poly(x,3,raw=TRUE))
> model
Call:
lm(formula = y ~ poly(x, 3, raw = TRUE))
Coefficients:
(Intercept) poly(x, 3, raw = TRUE)1 poly(x, 3, raw = TRUE)2 poly(x, 3, raw = TRUE)3
6.6096981 1.4736619 -0.0238935 0.0002445
Since you have fitted a low order polynomial in ordinary form (raw = TRUE), you can use polyroot to directly find x given y.
## pc: polynomial coefficients in increasing order
solvePC <- function (pc, y) {
pc[1] <- pc[1] - y
## all roots, including complex ones
roots <- polyroot(pc)
## keep real roots
Re(roots)[abs(Im(roots)) / Mod(roots) < 1e-10]
}
y0 <- 38.9 ## example y-value
x0 <- solvePC(coef(model), y0)
#[1] 34.28348
plot(x, y, col = 8)
lines(x, model$fitted, lwd = 2)
abline(h = y0)
abline(v = x0)
To get an interval estimate, we can use sampling methods.
## polyfit: an ordinary polynomial regression model fitted by lm()
rootCI <- function (polyfit, y, nSamples = 1000, level = 0.05) {
## sample regression coefficients from their joint distribution
pc <- MASS::mvrnorm(nSamples, coef(polyfit), vcov(polyfit))
## for each row (a sample), call solvePC()
roots <- apply(pc, 1, solvePC, y)
## confidence interval
quantile(roots, prob = c(0.5 * level, 1 - 0.5 * level))
}
## 95% confidence interval
rootCI(model, y = y0)
# 2.5% 97.5%
#34.17981 34.38828
You can use optim:
Predict the y values given x:
pred_y <- function(x)predict(model, data.frame(x))
pred_y(x = 10)
[1] 19.20145
Now to predict x given y, we do:
pred_x <- function(y) optim(1, \(x) (y-pred_y(x))^2, method='BFGS')[[1]]
pred_x(19.20145)
[1] 10
The uniroot function is intended for this type of problem.
#coefficients for the model
coeff <- c(6.6096981, 1.4736619, -0.0238935, 0.0002445)
#define the equation which one needs the root of
modely <- function(x, y) {
# could use the predict function here
my<-coeff[1] + coeff[2]*x + coeff[3]*x**2 + coeff[4]*x**3
y-my
}
#use the uniroot functiion
#In this example y=10
uniroot(modely, lower=-100, upper=100, y=10)
$root
[1] 2.391022
$f.root
[1] -1.208443e-08
$iter
[1] 10
$init.it
[1] NA
$estim.prec
[1] 6.103516e-05
In this case for y=10, x = 2.391022
I have two dataframes that have columns as such:
df1 <- c(1.11, 1.13, 1.12, 1.21, 1.22, 1.3, 1.4, 1.5, 2, 5, 10.1, 10.2,
10.3, 11.1, 11.2, 13.1, 13.2, 12, 14.1, 14.21, 14.22, 14.29,
15.11, 15.12, 15.13, 15.14, 15.2, 15.31, 15.32, 15.33, 15.42,
15.49, 15.41, 15.43, 15.44, 15.51, 15.52, 15.53, 15.54, 16, 17.11,
17.21, 17.12, 17.22, 17.23, 17.29, 17.3, 18.1, 18.2, 19.11, 19.12,
19.2, 20.1, 20.21, 20.22, 20.23, 20.29, 21.01, 21.02, 21.09,
22.12, 22.11, 22.13, 22.19, 22.21, 22.22, 22.3, 23.1, 23.2, 23.3,
24.11, 24.12, 24.13, 24.3, 24.23, 24.21, 24.24, 24.22, 24.29,
25.11, 25.19, 25.2, 26.1, 26.94, 26.95, 26.93, 26.92, 26.91,
26.96, 26.99, 27.1, 27.2, 27.31, 27.32, 28.11, 28.12, 28.13,
28.91, 28.92, 28.93, 28.99, 29.11, 29.12, 29.13, 29.14, 29.15,
29.19, 29.21, 29.22, 29.29, 29.24, 29.23, 29.25, 29.26, 29.27,
29.3, 30, 31.1, 31.2, 31.3, 31.4, 31.5, 31.9, 32.1, 32.2, 32.3,
33.11, 33.12, 33.13, 33.2, 33.3, 34.1, 34.2, 34.3, 35.11, 35.12,
35.2, 35.3, 35.91, 35.92, 35.99, 36.1, 36.91, 36.92, 36.93, 36.94,
36.99, 37.1, 37.2, 40.1, 40.2, 40.3, 41, 45.1, 45.2, 45.3, 45.4,
45.5, 50.1, 50.2, 50.3, 50.4, 50.5, 51.1, 51.21, 51.22, 51.31,
51.39, 51.41, 51.42, 51.43, 51.49, 51.5, 51.9, 52.11, 52.19,
52.2, 52.32, 52.31, 52.33, 52.34, 52.39, 52.4, 52.51, 52.52,
52.59, 52.6, 55.1, 55.2, 60.1, 60.21, 60.22, 60.23, 60.3, 61.1,
61.2, 62.1, 62.2, 63.01, 63.02, 63.03, 63.04, 63.09, 64.11, 64.12,
64.2, 65.11, 65.19, 65.91, 65.92, 65.99, 66.01, 66.03, 66.02,
67.11, 67.12, 67.19, 67.2, 70.1, 70.2, 71.11, 71.12, 71.13, 71.21,
71.22, 71.23, 71.29, 71.3, 72.1, 72.2, 72.3, 72.4, 72.5, 72.9,
73.1, 73.2, 74.11, 74.12, 74.13, 74.14, 74.21, 74.22, 74.3, 74.91,
74.92, 74.93, 74.94, 74.95, 74.99, 75.11, 75.12, 75.13, 75.14,
75.21, 75.22, 75.23, 75.3, 80.1, 80.21, 80.22, 80.3, 80.9, 85.11,
85.12, 85.19, 85.2, 85.31, 85.32, 90, 91.11, 91.12, 91.2, 91.91,
91.92, 91.99, 92.11, 92.12, 92.13, 92.14, 92.19, 92.2, 92.31,
92.32, 92.33, 92.41, 92.49, 93.01, 93.02, 93.03, 93.09, 95, 99
)
df2 <- c(111L, 112L, 113L, 121L, 122L, 130L, 140L, 200L, 1511L, 1549L,
1520L, 1513L, 1512L, 1514L, 1532L, 1531L, 1541L, 1544L, 1542L,
1543L, 150L, 501L, 502L, 1551L, 1552L, 1553L, 1554L, 9600L, 9700L,
2429L, 1533L, 1600L, 1810L, 1820L, 2330L, 2411L, 2412L, 2421L,
2413L, 2430L, 2519L, 2520L, 2010L, 2021L, 2022L, 2023L, 2029L,
1920L, 3699L, 2101L, 2102L, 2699L, 2109L, 1711L, 1712L, 1729L,
2610L, 5260L, 1721L, 1730L, 1722L, 1723L, 3720L, 1410L, 1429L,
1421L, 1422L, 1030L, 2710L, 2731L, 2891L, 2892L, 3520L, 3710L,
NA, 1310L, 1200L, 1320L, 2720L, 2732L, 1010L, 1020L, 2310L, 2320L,
1110L, 2422L, 2423L, 2424L, 2927L, 2914L, 2919L, 2929L, 3190L,
3311L, 3312L, 3313L, 3000L, 3320L, 3330L, 1911L, 1912L, 2899L,
2511L, 3140L, 3511L, 3512L, 3694L, 2692L, 2693L, 2694L, 2695L,
2696L, 2691L, 3691L, 3692L, 3693L, 2221L, 2926L, 3150L, 3592L,
2893L, 2915L, 2921L, 3610L, 2811L, 2812L, 2813L, 2930L, 3420L,
2912L, 2911L, 2922L, 2923L, 2924L, 2925L, 7250L, 2913L, 3599L,
3410L, 3430L, 3591L, 3530L, 3110L, 3120L, 3210L, 2213L, 2230L,
3220L, 3230L, 3130L, 2211L, 2212L, 2219L, 2222L)
How can I adjust the first one in order to use it to merge with the second? The first one is a character column, so that I would need to substitute the . out. The issue is that if I do such thing, a value such as 1.3 becomes 13 and not 130, as desired. If I multiply it by 10, then the other regular values wouldn't be matched.
You can use format(df1, nsmall = 2L) first, and then remove all of the ..
library(stringr)
library(dplyr) #for the pipe "%>%"
#>
#> Attaching package: 'dplyr'
#> The following objects are masked from 'package:stats':
#>
#> filter, lag
#> The following objects are masked from 'package:base':
#>
#> intersect, setdiff, setequal, union
df1 <- c(1.11, 1.13, 1.12, 1.21, 1.22, 1.3, 1.4, 1.5, 2, 5, 10.1, 10.2,
10.3, 11.1, 11.2, 13.1, 13.2, 12, 14.1, 14.21, 14.22, 14.29,
15.11, 15.12, 15.13, 15.14, 15.2, 15.31, 15.32, 15.33, 15.42,
15.49, 15.41, 15.43, 15.44, 15.51, 15.52, 15.53, 15.54, 16, 17.11,
17.21, 17.12, 17.22, 17.23, 17.29, 17.3, 18.1, 18.2, 19.11, 19.12,
19.2, 20.1, 20.21, 20.22, 20.23, 20.29, 21.01, 21.02, 21.09,
22.12, 22.11, 22.13, 22.19, 22.21, 22.22, 22.3, 23.1, 23.2, 23.3,
24.11, 24.12, 24.13, 24.3, 24.23, 24.21, 24.24, 24.22, 24.29,
25.11, 25.19, 25.2, 26.1, 26.94, 26.95, 26.93, 26.92, 26.91,
26.96, 26.99, 27.1, 27.2, 27.31, 27.32, 28.11, 28.12, 28.13,
28.91, 28.92, 28.93, 28.99, 29.11, 29.12, 29.13, 29.14, 29.15,
29.19, 29.21, 29.22, 29.29, 29.24, 29.23, 29.25, 29.26, 29.27,
29.3, 30, 31.1, 31.2, 31.3, 31.4, 31.5, 31.9, 32.1, 32.2, 32.3,
33.11, 33.12, 33.13, 33.2, 33.3, 34.1, 34.2, 34.3, 35.11, 35.12,
35.2, 35.3, 35.91, 35.92, 35.99, 36.1, 36.91, 36.92, 36.93, 36.94,
36.99, 37.1, 37.2, 40.1, 40.2, 40.3, 41, 45.1, 45.2, 45.3, 45.4,
45.5, 50.1, 50.2, 50.3, 50.4, 50.5, 51.1, 51.21, 51.22, 51.31,
51.39, 51.41, 51.42, 51.43, 51.49, 51.5, 51.9, 52.11, 52.19,
52.2, 52.32, 52.31, 52.33, 52.34, 52.39, 52.4, 52.51, 52.52,
52.59, 52.6, 55.1, 55.2, 60.1, 60.21, 60.22, 60.23, 60.3, 61.1,
61.2, 62.1, 62.2, 63.01, 63.02, 63.03, 63.04, 63.09, 64.11, 64.12,
64.2, 65.11, 65.19, 65.91, 65.92, 65.99, 66.01, 66.03, 66.02,
67.11, 67.12, 67.19, 67.2, 70.1, 70.2, 71.11, 71.12, 71.13, 71.21,
71.22, 71.23, 71.29, 71.3, 72.1, 72.2, 72.3, 72.4, 72.5, 72.9,
73.1, 73.2, 74.11, 74.12, 74.13, 74.14, 74.21, 74.22, 74.3, 74.91,
74.92, 74.93, 74.94, 74.95, 74.99, 75.11, 75.12, 75.13, 75.14,
75.21, 75.22, 75.23, 75.3, 80.1, 80.21, 80.22, 80.3, 80.9, 85.11,
85.12, 85.19, 85.2, 85.31, 85.32, 90, 91.11, 91.12, 91.2, 91.91,
91.92, 91.99, 92.11, 92.12, 92.13, 92.14, 92.19, 92.2, 92.31,
92.32, 92.33, 92.41, 92.49, 93.01, 93.02, 93.03, 93.09, 95, 99
)
df1 %>%
format(nsmall = 2L) %>%
as.character() %>%
str_remove('\\.')
#> [1] " 111" " 113" " 112" " 121" " 122" " 130" " 140" " 150" " 200" " 500"
#> [11] "1010" "1020" "1030" "1110" "1120" "1310" "1320" "1200" "1410" "1421"
#> [21] "1422" "1429" "1511" "1512" "1513" "1514" "1520" "1531" "1532" "1533"
#> [31] "1542" "1549" "1541" "1543" "1544" "1551" "1552" "1553" "1554" "1600"
#> [41] "1711" "1721" "1712" "1722" "1723" "1729" "1730" "1810" "1820" "1911"
#> [51] "1912" "1920" "2010" "2021" "2022" "2023" "2029" "2101" "2102" "2109"
#> [61] "2212" "2211" "2213" "2219" "2221" "2222" "2230" "2310" "2320" "2330"
#> [71] "2411" "2412" "2413" "2430" "2423" "2421" "2424" "2422" "2429" "2511"
#> [81] "2519" "2520" "2610" "2694" "2695" "2693" "2692" "2691" "2696" "2699"
#> [91] "2710" "2720" "2731" "2732" "2811" "2812" "2813" "2891" "2892" "2893"
#> [101] "2899" "2911" "2912" "2913" "2914" "2915" "2919" "2921" "2922" "2929"
#> [111] "2924" "2923" "2925" "2926" "2927" "2930" "3000" "3110" "3120" "3130"
#> [121] "3140" "3150" "3190" "3210" "3220" "3230" "3311" "3312" "3313" "3320"
#> [131] "3330" "3410" "3420" "3430" "3511" "3512" "3520" "3530" "3591" "3592"
#> [141] "3599" "3610" "3691" "3692" "3693" "3694" "3699" "3710" "3720" "4010"
#> [151] "4020" "4030" "4100" "4510" "4520" "4530" "4540" "4550" "5010" "5020"
#> [161] "5030" "5040" "5050" "5110" "5121" "5122" "5131" "5139" "5141" "5142"
#> [171] "5143" "5149" "5150" "5190" "5211" "5219" "5220" "5232" "5231" "5233"
#> [181] "5234" "5239" "5240" "5251" "5252" "5259" "5260" "5510" "5520" "6010"
#> [191] "6021" "6022" "6023" "6030" "6110" "6120" "6210" "6220" "6301" "6302"
#> [201] "6303" "6304" "6309" "6411" "6412" "6420" "6511" "6519" "6591" "6592"
#> [211] "6599" "6601" "6603" "6602" "6711" "6712" "6719" "6720" "7010" "7020"
#> [221] "7111" "7112" "7113" "7121" "7122" "7123" "7129" "7130" "7210" "7220"
#> [231] "7230" "7240" "7250" "7290" "7310" "7320" "7411" "7412" "7413" "7414"
#> [241] "7421" "7422" "7430" "7491" "7492" "7493" "7494" "7495" "7499" "7511"
#> [251] "7512" "7513" "7514" "7521" "7522" "7523" "7530" "8010" "8021" "8022"
#> [261] "8030" "8090" "8511" "8512" "8519" "8520" "8531" "8532" "9000" "9111"
#> [271] "9112" "9120" "9191" "9192" "9199" "9211" "9212" "9213" "9214" "9219"
#> [281] "9220" "9231" "9232" "9233" "9241" "9249" "9301" "9302" "9303" "9309"
#> [291] "9500" "9900"
Created on 2020-02-22 by the reprex package (v0.3.0)
Multiply each element in the first column by 100 after turning it into a numeric.
That is,
as.numeric(df1)*100
First I estimated the parameters of exponentiated generalized normal distribution using the dataset (data1: generated from normal distribution). Then I used real dataset (data2) and tried to find the maximum likelihood estimates (MLE) using the AdequacyModel packages. It gives the error message (mentioned right below the code).
Why does the same code estimate for first dataset (data1), but it doesn't estimate for the second dataset (data2)?
Is my way of plugging the baseline distribution (normal) in generalized class of distributions F(x)= [1-(1-G(x))^beta]^gamma introduced by Cordeiro et al.(2013) in R environment right? Am I defining the cdf and pdf of an generalized normal distribution in R in right way?
# For first dataset
data1 <- rnorm(100)
pdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( beta*gamma* ((1-(1-(pnorm(x,mean,sd)))^beta)^(gamma-1)) * ((1-
(pnorm(x,mean,sd)))^(beta-1)) ) * (dnorm(x,mean,sd))
}
cdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( 1-(1-(pnorm(x,mean,sd)))^beta)^gamma
}
set.seed(1)
result = goodness.fit(pdf = pdf_exps, cdf = cdf_exps,
starts = c(1,1,1,1),data = data1 , method = "BFGS",
domain = c(-Inf,Inf), lim_inf = c(0,0,0,0),
lim_sup = c(2,2,2,2), S = 250, prop=0.1, N=50)
result$mle
[1] 0.5976990 0.1541794 1.0073006 0.4689187
# For second data set
data2 <-c( 20.56, 20.67, 21.86, 21.88, 18.96, 21.04, 21.69, 20.62, 22.64, 19.44, 25.75, 21.20,
22.03, 25.44, 22.63, 21.86, 22.27, 21.27, 23.47, 23.19, 23.17, 24.54, 22.96, 19.76,
23.36, 22.67, 24.24, 24.21, 20.46, 20.81, 20.17, 23.06, 24.40, 23.97, 22.62, 19.16,
21.15, 21.40, 21.03, 21.77, 21.38, 21.47, 24.45, 22.63, 22.80, 23.58, 20.06, 23.01,
24.64, 18.26, 24.47, 23.99, 26.24, 20.04, 25.72, 25.64, 19.87, 23.35, 22.42, 20.42,
22.13, 25.17, 23.72, 21.28, 20.87, 19.00, 22.04, 20.12, 21.35, 28.57, 26.95, 28.13,
26.85, 25.27, 31.93, 16.75, 19.54, 20.42, 22.76, 20.12, 22.35, 19.16, 20.77, 19.37,
22.37, 17.54, 19.06, 20.30, 20.15, 25.36, 22.12, 21.25, 20.53, 17.06, 18.29, 18.37,
18.93, 17.79, 17.05, 20.31, 22.46, 23.88, 23.68, 23.15, 22.32, 24.02, 23.29, 25.11,
22.81, 26.25, 21.38, 22.52, 26.73, 23.57, 25.84, 24.06, 23.85, 25.09, 23.84, 25.31,
19.69, 26.07, 25.50, 23.69, 26.79, 25.61, 25.06, 24.93, 22.96, 20.69, 23.97, 24.64,
25.93, 23.69, 25.38, 22.68, 23.36, 22.44, 22.57, 19.81, 21.19, 20.39, 21.12, 21.89,
29.97, 27.39, 23.11, 21.75, 20.89, 22.83, 22.02, 20.07, 20.15, 21.24, 19.63, 23.58,
21.65, 25.17, 23.25, 32.52, 22.59, 30.18, 34.42, 21.86, 23.99, 24.81, 21.68, 21.04,
23.12, 20.76, 23.13, 22.35, 22.28, 23.55, 19.85, 26.51, 24.78, 33.73, 30.18, 23.31,
24.51, 25.37, 23.67, 24.28, 25.82, 21.93, 23.38, 23.07, 25.21, 23.25, 22.93, 26.86,
21.26, 25.43, 24.54, 27.79, 23.58, 27.56, 23.76, 22.01, 22.34, 21.07)
pdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( beta*gamma* ((1-(1-(pnorm(x,mean,sd)))^beta)^(gamma-1)) *
((1-(pnorm(x,mean,sd)))^(beta-1)) ) * (dnorm(x,mean,sd))
}
cdf_exps <- function(par,x){
beta = par[1]
gamma= par[2]
mean = par[3]
sd = par[4]
( 1-(1-(pnorm(x,mean,sd)))^beta)^gamma
}
set.seed(1)
result = goodness.fit(pdf = pdf_exps, cdf = cdf_exps,
starts = c(1,1,1,1),data = data2 , method = "BFGS",
domain = c(-Inf,Inf), lim_inf = c(0,0,0,0),
lim_sup = c(2,2,2,2), S = 250, prop=0.1, N=50)
result$mle
Error in optim(par = starts, fn = likelihood, x = data, method = "BFGS",
:non-finite finite-difference value [1]
I have a very stylized line chart and I would like to plot all my lines in with one add_trace-command, in the hope that this makes my code neater.
I have two issues:
I want a lower opacity for the high-lines and full opacity for the low lines. If I try it seems to assign the opacity randomly.
I want the upper lines to be solid and the lower ones to be dashed. The opposite happens.
Concerning these issues I have two questions:
Can this 'strange' (not logical) behaviour of plotly be fixed? Maybe by using some layout option?
Does this 'strange' behaviour occur because I am trailing of the path?
The plotly examples usually tell you to write a new add_trace function for every line or other object you had. I am trying to implement all my lines with one add_trace-function.
In my real data, I have more than ten lines to draw and it would really help if I could draw some of the lines together. Here are some sample graph and data:
I tried with this code:
month <- c('January', 'February', 'March', 'April', 'May', 'June', 'July',
'August', 'September', 'October', 'November', 'December')
high_2000 <- c(32.5, 37.6, 49.9, 53.0, 69.1, 75.4, 76.5, 76.6, 70.7, 60.6, 45.1, 29.3)
low_2000 <- c(13.8, 22.3, 32.5, 37.2, 49.9, 56.1, 57.7, 58.3, 51.2, 42.8, 31.6, 15.9)
high_2007 <- c(36.5, 26.6, 43.6, 52.3, 71.5, 81.4, 80.5, 82.2, 76.0, 67.3, 46.1, 35.0)
low_2007 <- c(23.6, 14.0, 27.0, 36.8, 47.6, 57.7, 58.9, 61.2, 53.3, 48.5, 31.0, 23.6)
high_2014 <- c(28.8, 28.5, 37.0, 56.8, 69.7, 79.7, 78.5, 77.8, 74.1, 62.6, 45.3, 39.9)
low_2014 <- c(12.7, 14.3, 18.6, 35.5, 49.9, 58.0, 60.0, 58.6, 51.7, 45.2, 32.2, 29.1)
data <- data.frame(month, high_2000, low_2000, high_2007, low_2007, high_2014, low_2014)
library(plotly)
df<-tidyr::gather(data,key,values,-month)
plot_ly(data=df,x=~month,y=~values,split=~key,type="scatter",
mode="lines",opacity=ifelse(grepl('high',df$key),0.5,1),line=list(color='#1f77b4'),
linetype=ifelse(grepl('2000',df$key),'solid','dashed')) %>%
layout(xaxis=list(categoryarray = month, categoryorder = "array"))
Does this work for you?
df$key <- as.factor(df$key)
df$key <- factor(df$key , levels = c("high_2014","high_2007", "high_2000", "low_2014","low_2007", "low_2000"))
df$high_low <- substr(df$key, 1, 2)
df$high_low <- factor(df$high_low , levels = c("hi","lo"))
df <- df %>% arrange(high_low)
plot_ly(data=df,x=~month,y=~values,split=~key,type="scatter", mode="lines", opacity=ifelse(grepl('high',df$key),0.5,1), line=list(color='#1f77b4'),
linetype= ~ high_low, linetypes = c('solid', 'dashed')) %>%
layout(xaxis=list(categoryarray = month, categoryorder = "array"))
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,
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27.28, 27.295, 27.288, 27.286, 27.279), soil_m_sat = c(24.1,
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"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