I have been spending FAR too much time trying to figure this out - so time to seek help. I am attempting to use lmfit to fit two lognormals (a and c) as well as the sum of these two lognormals (a+c) to a size distribution. Mode a centers around x=0.2, y=1, mode c centers around x=1.2, y=<<<1. There are numerous size distributions (>200) which are all slightly different and are passed in to the following code from an outside loop. For this example, I have provided a real life distribution and have not included the loop. Hopefully my code is sufficiently annotated to allow understanding of what I am trying to achieve.
I must be missing some fundamental understanding of lmfit (spoiler alert - I'm not great at Maths either) as I have 2 problems:
the fits (a, c and a+c) do not accurately represent the data. Note how the fit (red solid line) diverts away from the data (blue solid line). I assume this is something to do with the initial guess parameters. I have tried LOTS and have been unable to get a good fit.
re-running the model with "new" best fit values (results2, results3) doesn't appear to significantly improve the fit at all. Why?
Example result using provided x and y data:
Here is one-I-made-earlier showing the type of fit I am after (produced using the older mpfit module, using different data than provided below and using unique initial best guess parameters (not in a loop). Excuse the legend format, I had to remove certain information):
Any assistance is much appreciated. Here is the code with an example distribution:
from lmfit import models
import matplotlib.pyplot as plt
import numpy as np
# real life data example
y = np.array([1.000000, 0.754712, 0.610303, 0.527856, 0.412125, 0.329689, 0.255756, 0.184424, 0.136819,
0.102316, 0.078763, 0.060896, 0.047118, 0.020297, 0.007714, 0.010202, 0.008710, 0.005579,
0.004644, 0.004043, 0.002618, 0.001194, 0.001263, 0.001043, 0.000584, 0.000330, 0.000179,
0.000117, 0.000050, 0.000035, 0.000017, 0.000007])
x = np.array([0.124980, 0.130042, 0.135712, 0.141490, 0.147659, 0.154711, 0.162421, 0.170855, 0.180262,
0.191324, 0.203064, 0.215738, 0.232411, 0.261810, 0.320252, 0.360761, 0.448802, 0.482528,
0.525526, 0.581518, 0.658988, 0.870114, 1.001815, 1.238899, 1.341285, 1.535134, 1.691963,
1.973359, 2.285620, 2.572177, 2.900414, 3.342739])
# create the joint model using prefixes for each mode
model = (models.LognormalModel(prefix='p1_') +
models.LognormalModel(prefix='p2_'))
# add some best guesses for the model parameters
params = model.make_params(p1_center=0.1, p1_sigma=2, p1_amplitude=1,
p2_center=1, p2_sigma=2, p2_amplitude=0.000000000000001)
# bound those best guesses
# params['p1_amplitude'].min = 0.0
# params['p1_amplitude'].max = 1e5
# params['p1_sigma'].min = 1.01
# params['p1_sigma'].max = 5
# params['p1_center'].min = 0.01
# params['p1_center'].max = 1.0
#
# params['p2_amplitude'].min = 0.0
# params['p2_amplitude'].max = 1
# params['p2_sigma'].min = 1.01
# params['p2_sigma'].max = 10
# params['p2_center'].min = 1.0
# params['p2_center'].max = 3
# actually fit the model
result = model.fit(y, params, x=x)
# ====================================
# ================================
# re-run using the best-fit params derived above
params2 = model.make_params(p1_center=result.best_values['p1_center'], p1_sigma=result.best_values['p1_sigma'],
p1_amplitude=result.best_values['p1_amplitude'],
p2_center=result.best_values['p2_center'], p2_sigma=result.best_values['p2_sigma'],
p2_amplitude=result.best_values['p2_amplitude'], )
# re-fit the model
result2 = model.fit(y, params2, x=x)
# ================================
# re-run again using the best-fit params derived above
params3 = model.make_params(p1_center=result2.best_values['p1_center'], p1_sigma=result2.best_values['p1_sigma'],
p1_amplitude=result2.best_values['p1_amplitude'],
p2_center=result2.best_values['p2_center'], p2_sigma=result2.best_values['p2_sigma'],
p2_amplitude=result2.best_values['p2_amplitude'], )
# re-fit the model
result3 = model.fit(y, params3, x=x)
# ================================
# add individual fine and coarse modes using the revised fit parameters
model_a = models.LognormalModel()
params_a = model_a.make_params(center=result3.best_values['p1_center'], sigma=result3.best_values['p1_sigma'],
amplitude=result3.best_values['p1_amplitude'])
result_a = model_a.fit(y, params_a, x=x)
model_c = models.LognormalModel()
params_c = model_c.make_params(center=result3.best_values['p2_center'], sigma=result3.best_values['p2_sigma'],
amplitude=result3.best_values['p2_amplitude'])
result_c = model_c.fit(y, params_c, x=x)
# ====================================
plt.plot(x, y, 'b-', label='data')
plt.plot(x, result.best_fit, 'r-', label='best_fit_1')
plt.plot(x, result.init_fit, 'lightgrey', ls=':', label='ini_fit_1')
plt.plot(x, result2.best_fit, 'r--', label='best_fit_2')
plt.plot(x, result2.init_fit, 'lightgrey', ls='--', label='ini_fit_2')
plt.plot(x, result3.best_fit, 'r.-', label='best_fit_3')
plt.plot(x, result3.init_fit, 'lightgrey', ls='--', label='ini_fit_3')
plt.plot(x, result_a.best_fit, 'grey', ls=':', label='best_fit_a')
plt.plot(x, result_c.best_fit, 'grey', ls='--', label='best_fit_c')
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()
There are three main pieces of advice I can give:
initial values matter and should not be so far off as to make
portions of the model completely insensitive to the parameter
values. Your initial model is sort of off by several orders of
magnitude.
always look at the fit result. This is the primary
result -- the plot of the fit is a representation of the actual
numerical results. Not showing that you printed out the fit
report is a good indication that you did not look at the actual
result. Really, always look at the results.
if you are judging the quality of the fit based on a plot of
the data and model, use how you choose to plot the data to guide
how you fit the data. Specifically in your case, if you are
plotting on a log scale, then fit the log of the data to the log
of the model: fit in "log space".
Such a fit might look like this:
from lmfit import models, Model
from lmfit.lineshapes import lognormal
import matplotlib.pyplot as plt
import numpy as np
y = np.array([1.000000, 0.754712, 0.610303, 0.527856, 0.412125, 0.329689, 0.255756, 0.184424, 0.136819,
0.102316, 0.078763, 0.060896, 0.047118, 0.020297, 0.007714, 0.010202, 0.008710, 0.005579,
0.004644, 0.004043, 0.002618, 0.001194, 0.001263, 0.001043, 0.000584, 0.000330, 0.000179,
0.000117, 0.000050, 0.000035, 0.000017, 0.000007])
x = np.array([0.124980, 0.130042, 0.135712, 0.141490, 0.147659, 0.154711, 0.162421, 0.170855, 0.180262,
0.191324, 0.203064, 0.215738, 0.232411, 0.261810, 0.320252, 0.360761, 0.448802, 0.482528,
0.525526, 0.581518, 0.658988, 0.870114, 1.001815, 1.238899, 1.341285, 1.535134, 1.691963,
1.973359, 2.285620, 2.572177, 2.900414, 3.342739])
# use a model that is the log of the sum of two log-normal functions
# note to be careful about log(x) for x < 0.
def log_lognormal(x, amp1, cen1, sig1, amp2, cen2, sig2):
comp1 = lognormal(x, amp1, cen1, sig1)
comp2 = lognormal(x, amp2, cen2, sig2)
total = comp1 + comp2
total[np.where(total<1.e-99)] = 1.e-99
return np.log(comp1+comp2)
model = Model(log_lognormal)
params = model.make_params(amp1=5.0, cen1=-4, sig1=1,
amp2=0.1, cen2=-1, sig2=1)
# part of making sure that the lognormals are strictly positive
params['amp1'].min = 0
params['amp2'].min = 0
result = model.fit(np.log(y), params, x=x)
print(result.fit_report()) # <-- HERE IS WHERE THE RESULTS ARE!!
# also, make a plot of data and fit
plt.plot(x, y, 'b-', label='data')
plt.plot(x, np.exp(result.best_fit), 'r-', label='best_fit')
plt.plot(x, np.exp(result.init_fit), 'grey', label='ini_fit')
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()
This will print out
[[Model]]
Model(log_lognormal)
[[Fit Statistics]]
# fitting method = leastsq
# function evals = 211
# data points = 32
# variables = 6
chi-square = 0.91190970
reduced chi-square = 0.03507345
Akaike info crit = -101.854407
Bayesian info crit = -93.0599914
[[Variables]]
amp1: 21.3565856 +/- 193.951379 (908.16%) (init = 5)
cen1: -4.40637490 +/- 3.81299642 (86.53%) (init = -4)
sig1: 0.77286862 +/- 0.55925566 (72.36%) (init = 1)
amp2: 0.00401804 +/- 7.5833e-04 (18.87%) (init = 0.1)
cen2: -0.74055538 +/- 0.13043827 (17.61%) (init = -1)
sig2: 0.64346873 +/- 0.04102122 (6.38%) (init = 1)
[[Correlations]] (unreported correlations are < 0.100)
C(amp1, cen1) = -0.999
C(cen1, sig1) = -0.999
C(amp1, sig1) = 0.997
C(cen2, sig2) = -0.964
C(amp2, cen2) = -0.940
C(amp2, sig2) = 0.849
C(sig1, amp2) = -0.758
C(cen1, amp2) = 0.740
C(amp1, amp2) = -0.726
C(sig1, cen2) = 0.687
C(cen1, cen2) = -0.669
C(amp1, cen2) = 0.655
C(sig1, sig2) = -0.598
C(cen1, sig2) = 0.581
C(amp1, sig2) = -0.567
and generate a plot like
I am running a logistic generalized linear mixed model and would like to plot my effects together with confidence intervals.
I use the lme4 package to fit my model:
glmer (cbind(positive, negative) ~ F1 * F2 * F3 + V1 + F1 * I(V1^2) + V2 + F1 * I(V2^2) + V3 + I(V3^2) + V4 + I(V4^2) + F4 + (1|OLRE) + (1|ind), family = binomial, data = try, na.action = na.omit, control=glmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "nlminb", starttests = FALSE, kkt = FALSE)))
OLRE means that I use an observational level random effect in order to overcome overdispersion.
If you wonder because of convergence warnings, I went through the lme4 troubleshooting protocol, and it should be fine.
In order to get effect plots with confidence intervals, I tried to use ggpredict:
sjPlot, e.g.:
plot_model(mod, type = "pred", terms = c("F1", "F2", "F3"), ci.lvl = 0.95)
I also tried to go through this protocol:
https://rpubs.com/hughes/84484
intdata <- expand.grid(
positive = c(0,1),
negative = c(0,1),
F1 = as.factor(c(0,1)),
F2 = as.factor(c(1,2,3)),
F3= as.factor(c(1,2,3,4)),
V1= as.numeric(median(try$V1)),
F4= as.factor(c(30, 31)),
ind= as.factor(c(68)),
OLRE = as.factor(c(2450)),
V2= as.numeric(median(try$V2)),
V3= as.numeric(median(try$V3)),
V4= as.numeric(median(try$V4))
)
#conditional variances
cV <- ranef(mod, condVar = TRUE)
ranvar <- attr(cV[[1]], "postVar")
sqrt(diag(ranvar[,,1]))
mm <- model.matrix(terms( mod), data=intdata,
contrasts.arg = lapply(intdata[,c(3:5, 7:9)], contrasts, contrasts=FALSE))
predFun<-function(.) mm%*%fixef(.)
bb<-bootMer(mod,FUN=predFun,nsim=3)
with some problems and warnings regarding contrasts and
Error in mm %*% fixef(.) : non-conformable arguments
Therefore, I am wondering if anyone might help me but so far I am not able to Nothing worked so far, so I would really appreciate some help.
Here the link to the data https://drive.google.com/file/d/1qZaJBbM1ggxwPnZ9bsTCXL7_BnXlvfkW/view?usp=sharing
I feel I must be missing something obvious, in struggling to get a positive control for logistic regression going in tensorflow probability.
I've modified the example for logistic regression here, and created a positive control features and labels data. I struggle to achieve accuracy over 60%, however this is an easy problem for a 'vanilla' Keras model (accuracy 100%). What am I missing? I tried different layers, activations, etc.. With this method of setting up the model, is posterior updating actually being performed? Do I need to specify an interceptor object? Many thanks..
### Added positive control
nSamples = 80
features1 = np.float32(np.hstack((np.reshape(np.ones(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features2 = np.float32(np.hstack((np.reshape(np.zeros(40), (40, 1)),
np.reshape(np.random.randn(nSamples), (40, 2)))))
features = np.vstack((features1, features2))
labels = np.concatenate((np.zeros(40), np.ones(40)))
featuresInt, labelsInt = build_input_pipeline(features, labels, 10)
###
#w_true, b_true, features, labels = toy_logistic_data(FLAGS.num_examples, 2)
#featuresInt, labelsInt = build_input_pipeline(features, labels, FLAGS.batch_size)
with tf.name_scope("logistic_regression", values=[featuresInt]):
layer = tfp.layers.DenseFlipout(
units=1,
activation=None,
kernel_posterior_fn=tfp.layers.default_mean_field_normal_fn(),
bias_posterior_fn=tfp.layers.default_mean_field_normal_fn())
logits = layer(featuresInt)
labels_distribution = tfd.Bernoulli(logits=logits)
neg_log_likelihood = -tf.reduce_mean(labels_distribution.log_prob(labelsInt))
kl = sum(layer.losses)
elbo_loss = neg_log_likelihood + kl
predictions = tf.cast(logits > 0, dtype=tf.int32)
accuracy, accuracy_update_op = tf.metrics.accuracy(
labels=labelsInt, predictions=predictions)
with tf.name_scope("train"):
optimizer = tf.train.AdamOptimizer(learning_rate=FLAGS.learning_rate)
train_op = optimizer.minimize(elbo_loss)
init_op = tf.group(tf.global_variables_initializer(),
tf.local_variables_initializer())
with tf.Session() as sess:
sess.run(init_op)
# Fit the model to data.
for step in range(FLAGS.max_steps):
_ = sess.run([train_op, accuracy_update_op])
if step % 100 == 0:
loss_value, accuracy_value = sess.run([elbo_loss, accuracy])
print("Step: {:>3d} Loss: {:.3f} Accuracy: {:.3f}".format(
step, loss_value, accuracy_value))
### Check with basic Keras
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1)])
optimizer = tf.train.AdamOptimizer(5e-2)
kerasModel.compile(optimizer = optimizer, loss = 'binary_crossentropy',
metrics = ['accuracy'])
kerasModel.fit(features, labels, epochs = 50) #100% accuracy
Compared to the github example, you forgot to divide by the number of examples when defining the KL divergence:
kl = sum(layer.losses) / FLAGS.num_examples
When I change this to your code, I quickly get to an accuracy of 99.9% on your toy data.
Additionaly, the output layer of your Keras model actually expects a sigmoid activation for this problem (binary classification):
kerasModel = tf.keras.models.Sequential([
tf.keras.layers.Dense(1, activation='sigmoid')])
It's a toy problem, but you will notice that the model gets to 100% accuracy faster with a sigmoid activation.
I'm creating a shiny app and i'm letting the user choose what data that should be displayed in a plot and a table. This choice is done through 3 different input variables that contain 14, 4 and two choices respectivly.
ui <- dashboardPage(
dashboardHeader(),
dashboardSidebar(
selectInput(inputId = "DataSource", label = "Data source", choices =
c("Restoration plots", "all semi natural grasslands")),
selectInput(inputId = "Variabel", label = "Variable", choices =
choicesVariables)),
#choicesVariables definition is omitted here, because it's very long but it
#contains 14 string values
selectInput(inputId = "Factor", label = "Factor", choices = c("Company
type", "Region and type of application", "Approved or not approved
applications", "Age group" ))
),
dashboardBody(
plotOutput("thePlot"),
tableOutput("theTable")
))
This adds up to 73 choices (yes, i know the math doesn't add up there, but some choices are invalid). I would like to do this using a lookup table so a created one with every valid combination of choices like this:
rad1<-c(rep("Company type",20), rep("Region and type of application",20),
rep("Approved or not approved applications", 13), rep("Age group", 20))
rad2<-choicesVariable[c(1:14,1,4,5,9,10,11, 1:14,1,4,5,9,10,11, 1:7,9:14,
1:14,1,4,5,9,10,11)]
rad3<-c(rep("Restoration plots",14),rep("all semi natural grasslands",6),
rep("Restoration plots",14), rep("all semi natural grasslands",6),
rep("Restoration plots",27), rep("all semi natural grasslands",6))
rad4<-1:73
letaLista<-data.frame(rad1,rad2,rad3, rad4)
colnames(letaLista) <- c("Factor", "Variabel", "rest_alla", "id")
Now its easy to use subset to only get the choice that the user made. But how do i use this information to plot the plot and table without using a 73 line long ifelse statment?
I tried to create some sort of multidimensional array that could hold all the tables (and one for the plots) but i couldn't make it work. My experience with these kind of arrays is limited and this might be a simple issue, but any hints would be helpful!
My dataset that is the foundation for the plots and table consists of dataframe with 23 variables, factors and numerical. The plots and tabels are then created using the following code for all 73 combinations
s_A1 <- summarySE(Samlad_info, measurevar="Dist_brukcentrum",
groupvars="Companytype")
s_A1 <- s_A1[2:6,]
p_A1=ggplot(s_A1, aes(x=Companytype,
y=Dist_brukcentrum))+geom_bar(position=position_dodge(), stat="identity") +
geom_errorbar(aes(ymin=Dist_brukcentrum-se,
ymax=Dist_brukcentrum+se),width=.2,position=position_dodge(.9))+
scale_y_continuous(name = "") + scale_x_discrete(name = "")
where summarySE is the following function, burrowed from cookbook for R
summarySE <- function(data=NULL, measurevar, groupvars=NULL, na.rm=TRUE,
conf.interval=.95, .drop=TRUE) {
# New version of length which can handle NA's: if na.rm==T, don't count them
length2 <- function (x, na.rm=FALSE) {
if (na.rm) sum(!is.na(x))
else length(x)
}
# This does the summary. For each group's data frame, return a vector with
# N, mean, and sd
datac <- ddply(data, groupvars, .drop=.drop,
.fun = function(xx, col) {
c(N = length2(xx[[col]], na.rm=na.rm),
mean = mean (xx[[col]], na.rm=na.rm),
sd = sd (xx[[col]], na.rm=na.rm)
)
},
measurevar
)
# Rename the "mean" column
datac <- rename(datac, c("mean" = measurevar))
datac$se <- datac$sd / sqrt(datac$N) # Calculate standard error of the mean
# Confidence interval multiplier for standard error
# Calculate t-statistic for confidence interval:
# e.g., if conf.interval is .95, use .975 (above/below), and use df=N-1
ciMult <- qt(conf.interval/2 + .5, datac$N-1)
datac$ci <- datac$se * ciMult
return(datac)
}
The code in it's entirety is a bit to large but i hope this may clarify what i'm trying to do.
Well, thanks to florian's comment i think i might have found a solution my self. I'll present it here but leave the question open as there is probably far neater ways of doing it.
I rigged up the plots (that was created as lists by ggplot) into a list
plotList <- list(p_A1, p_A2, p_A3...)
tableList <- list(s_A1, s_A2, s_A3...)
I then used subset on my lookup table to get the matching id of the list to select the right plot and table.
output$thePlot <-renderPlot({
plotValue<-subset(letaLista, letaLista$Factor==input$Factor &
letaLista$Variabel== input$Variabel & letaLista$rest_alla==input$DataSource)
plotList[as.integer(plotValue[1,4])]
})
output$theTable <-renderTable({
plotValue<-subset(letaLista, letaLista$Factor==input$Factor &
letaLista$Variabel== input$Variabel & letaLista$rest_alla==input$DataSource)
skriva <- tableList[as.integer(plotValue[4])]
print(skriva)
})