Difference between revisions of "SMHS LinearModeling MachineLearning"

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{| class="wikitable" style="text-align:center; width:35%" border="1"
 +
|-
 +
|Index||Subject||Day||Treatment||Obs
 +
|-
 +
|1||13||Day1||B||6.472687
 +
|-
 +
|2||14||Day1||B||7.01711
 +
|-
 +
|3||15||Day1||B||6.200715
 +
|-
 +
|4||16||Day1||B||6.613928
 +
|-
 +
|5||17||Day1||A||6.829968
 +
|-
 +
|6||18||Day1||A||7.387583
 +
|-
 +
|7||19||Day1||A||7.367293
 +
|-
 +
|8||20||Day1||A||8.018853
 +
|-
 +
|9||21||Day1||C||7.527408
 +
|-
 +
|10||22||Day1||C||6.746739
 +
|-
 +
|11||23||Day1||C||7.29691
 +
|-
 +
|12||24||Day1||C||6.98336
 +
|-
 +
|13||29||Day1||B||6.816621
 +
|-
 +
|14||30||Day1||B||6.571689
 +
|-
 +
|15||31||Day1||B||5.911261
 +
|-
 +
|16||32||Day1||B||6.954988
 +
|-
 +
|17||33||Day1||C||7.624122
 +
|-
 +
|18||34||Day1||C||7.669865
 +
|-
 +
|19||35||Day1||C||7.676225
 +
|-
 +
|20||36||Day1||C||7.263593
 +
|-
 +
|21||37||Day1||A||7.704737
 +
|-
 +
|22||38||Day1||A||7.328716
 +
|-
 +
|23||39||Day1||A||7.29561
 +
|-
 +
|24||40||Day1||A||5.96418
 +
|-
 +
|25||62||Day1||A||6.880814
 +
|-
 +
|26||63||Day1||A||6.926342
 +
|-
 +
|27||64||Day1||A||6.926342
 +
|-
 +
|28||65||Day1||A||7.562293
 +
|-
 +
|29||13||Day3||B||6.677607
 +
|-
 +
|30||14||Day3||B||7.023526
 +
|-
 +
|31||15||Day3||B||6.441864
 +
|-
 +
|32||16||Day3||B||7.020875
 +
|-
 +
|33||17||Day3||A||7.478931
 +
|-
 +
|34||18||Day3||A||7.495336
 +
|-
 +
|35||19||Day3||A||7.427709
 +
|-
 +
|36||20||Day3||A||7.63302
 +
|-
 +
|37||21||Day3||C||7.382091
 +
|-
 +
|38||22||Day3||C||7.359731
 +
|-
 +
|39||23||Day3||C||7.285889
 +
|-
 +
|40||24||Day3||C||7.496863
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|-
 +
|41||29||Day3||B||6.632403
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|-
 +
|42||30||Day3||B||6.171196
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|-
 +
|43||31||Day3||B||6.306012
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|-
 +
|44||32||Day3||B||7.253833
 +
|-
 +
|45||33||Day3||C||7.594852
 +
|-
 +
|46||34||Day3||C||6.915225
 +
|-
 +
|47||35||Day3||C||7.220147
 +
|-
 +
|48||36||Day3||C||7.298227
 +
|-
 +
|49||37||Day3||A||7.573612
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|-
 +
|50||38||Day3||A||7.36655
 +
|-
 +
|51||39||Day3||A||7.560513
 +
|-
 +
|52||40||Day3||A||7.289078
 +
|-
 +
|53||62||Day3||A||7.287802
 +
|-
 +
|54||63||Day3||A||7.155336
 +
|-
 +
|55||64||Day3||A||7.394452
 +
|-
 +
|56||65||Day3||A||7.465383
 +
|-
 +
|57||13||Day6||B||6.976048
 +
|-
 +
|58||14||Day6||B||7.222966
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|-
 +
|59||15||Day6||B||6.584153
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|-
 +
|60||16||Day6||B||7.013223
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|-
 +
|61||17||Day6||A||7.569905
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|-
 +
|62||18||Day6||A||7.459185
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|-
 +
|63||19||Day6||A||7.504068
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|-
 +
|64||20||Day6||A||7.801867
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|-
 +
|65||21||Day6||C||7.598728
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|-
 +
|66||22||Day6||C||7.475841
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|-
 +
|67||23||Day6||C||7.511873
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|-
 +
|68||24||Day6||C||7.518384
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|-
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|69||29||Day6||B||6.618589
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|-
 +
|70||30||Day6||B||5.854754
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|-
 +
|71||31||Day6||B||6.125749
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|-
 +
|72||32||Day6||B||6.96272
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|-
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|73||33||Day6||C||7.5406
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|-
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|74||34||Day6||C||7.379861
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|-
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|75||35||Day6||C||7.344189
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|-
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|76||36||Day6||C||7.362815
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|-
 +
|77||37||Day6||A||7.805802
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|-
 +
|78||38||Day6||A||7.764172
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|-
 +
|79||39||Day6||A||7.789844
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|-
 +
|80||40||Day6||A||7.616437
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|-
 +
|81||62||Day6||A||NA
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|-
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|82||63||Day6||A||NA
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|-
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|83||64||Day6||A||NA
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|-
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|84||65||Day6||A||NA
  
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|}
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</center>
 
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Revision as of 09:36, 4 March 2016

SMHS Linear Modeling - Machine Learning Algorithms

Scientific inference based on fixed and random effect models, assumptions, and mixed effects logistic regression.

Questions:

  • How can we tie human intuition and computer-generated results to obtain reliable, effective, and efficient decision-support system (that facilitates, forecasting)?
  • Niels Born – “It is difficult to make predictions, especially about the future” …
  • Can we unsupervisely classify the data?

Prediction

For most of the machine learning algorithms (including first-order linear regression), we:

  • first generate the model using training data, and then
  • predict values for test/new data.

Predictions are made using the R predict function. (type ?predict.name), where name is the function-name corresponding to the algorithm. The first argument of predict often represents the variable storing the model and the second argument is a matrix or data frame of test data that the model needs to be applied to. Calling predict can be done in 2 ways: type predict or type of predict.name.

Example: 

#mydata <- read.table('https://umich.instructure.com/files/330381/download?download_frd=1&verifier=HpfmjfMFaMsk7rIpfPx0tmz960oTW7JA8ZonGvVC',as.is=T, header=T)  # 01a_data.txt
# mydata <- read.table('data.txt',as.is=T, header=T)

# (1) First, there are different approaches to split the data (partition the data) into 
# training and testing sets.
## TRAINING: 75% of the sample size
sample_size <- floor(0.75 * nrow(mydata))
## set the seed to make your partition reproductible
set.seed(1234)
train_ind <- sample(seq_len(nrow(mydata)), size = sample_size)
train <- mydata[train_ind, ]

# TESTING DATA
test <- mydata[-train_ind, ]

lin.mod <- lm(Weight ~ Height*Team, data=train)
predicted.values <-  predict(lin.mod, newdata=test

Data Modeling/Training

Logistic Regression: 

glm_model <-glm(ifelse(Weight > 200,1,0) ~ Height*Team, family=binomial(link="logit"), data=train)

K-Means Clustering 

train.1 <- cbind(train$\$$Height, train$\$$Weight, train$\$$Age)
 test.1 <- cbind(test$\$$Height, test$\$$Weight, test$\$$Age)
Weight.1 <- ifelse(train$\$$Weight > 200,1,0)

 head(train.1)
 kmeans_model <- kmeans(<u><b>train.1</b></u>, 3)
 plot(train.1, col = kmeans_model$\$$cluster)
points(kmeans_model$\$$centers, col = 1:2, pch = 8, cex = 2)

<b>K-Nearest Neighbor Classification</b>
 # install.packages("class")
 library("class")
 knn_model  <-  knn(train=train.1,  test=test.1,  cl=as.factor(Weight.1),  k=5)
 plot(knn_model)
 summary(knn_model)

<b>Naïve Bayes Classifier</b>
 install.packages("e1071")
 library("e1071")
 nbc_model <-  naiveBayes(Weight ~ Height*Age,  data=train.1)

<b>Decision Trees (CART)</b>
 #install.packages("e1071")
 library("rpart")
 cart_model <- rpart(Weight ~ Height+Age, data= as.data.frame(train.1), method="class")
 plot(cart_model)
 text(cart_model) 

<b>AdaBoost</b>
 install.packages("ada")
 # X be the matrix of features, and labels be a vector of 0-1 class labels.
 library("ada")
 boost_model <- ada(x= cbind(train$\$$Height, train$\$$Weight, train$\$$Age), y= Weight.1)
plot(boost_model)
boost_model

Support Vector Machines (SVM) 

#install.packages("e1071")
library("rpart")
svm_model <- svm(x= cbind(train$\$$Height, train$\$$Weight, train$\$$Age), y=as.factor(Weight.1), 
kernel ="radial")
summary(svm_model)

Appendix

Example 1: Simulation (subject, day, treatment, observation)

Obs ~ Treatment + Day + Subject(Treatment)+ Day*Subject(Treatment)+ ε.

This model is accounts for:

Response = Obs

Fixed effects:

Treatment (fixed)

Day (fixed)

Treatment*Day interaction

Random Effects:

Subject nested within Treatment (random)

Day crossed with "Subject within Treatment" (random) 

mydata <- data.frame(
Subject  = c(13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 
34, 35, 36, 37, 38, 39, 40, 62, 63, 64, 65, 13, 14, 15, 16, 17, 18, 
19, 20, 21, 22, 23, 24, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 
40, 62, 63, 64, 65, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 
29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 62, 63, 64, 65), 
Day       = c(rep(c("Day1", "Day3", "Day6"), each=28)), 
Treatment = c(rep(c("B", "A", "C", "B", "C", "A", "A", "B", "A", "C", "B", "C", 
"A", "A", "B", "A", "C", "B", "C", "A", "A"), each = 4)), 
Obs       = c(6.472687, 7.017110, 6.200715, 6.613928, 6.829968, 7.387583, 7.367293, 
8.018853, 7.527408, 6.746739, 7.296910, 6.983360, 6.816621, 6.571689, 
5.911261, 6.954988, 7.624122, 7.669865, 7.676225, 7.263593, 7.704737, 
7.328716, 7.295610, 5.964180, 6.880814, 6.926342, 6.926342, 7.562293, 
6.677607, 7.023526, 6.441864, 7.020875, 7.478931, 7.495336, 7.427709, 
7.633020, 7.382091, 7.359731, 7.285889, 7.496863, 6.632403, 6.171196, 
6.306012, 7.253833, 7.594852, 6.915225, 7.220147, 7.298227, 7.573612, 
7.366550, 7.560513, 7.289078, 7.287802, 7.155336, 7.394452, 7.465383, 
6.976048, 7.222966, 6.584153, 7.013223, 7.569905, 7.459185, 7.504068, 
7.801867, 7.598728, 7.475841, 7.511873, 7.518384, 6.618589, 5.854754, 
6.125749, 6.962720, 7.540600, 7.379861, 7.344189, 7.362815, 7.805802, 
7.764172, 7.789844, 7.616437, NA, NA, NA, NA))

install.packages("lme4")
library("lme4", lib.loc="~/R/win-library/3.1")
m1 <- lmer(Obs ~ Treatment * Day + (1 | Subject), mydata)
m1

Linear mixed model fit by REML ['lmerMod']

Formula: Obs ~ Treatment * Day + (1 | Subject)

Data: mydata

REML criterion at convergence: 56.8669

Random Effects
Groups Name Std. Dev.
Subject (Intercept) 0.2163
Residual 0.2602
Number of obs: 80, groups: Subject, 28



Fixed Effects
(Intercept) TreatmentB TreatmentC
7.1827 -0.6129 0.1658
DayDay3 DayDay6 TreatmentB: DayDay3
0.2446 0.4507 -0.1235
TreatmentC: DayDay3 TreatmentB: DayDay6 TreatmentC: DayDay6



Index Subject Day Treatment Obs
1 13 Day1 B 6.472687
2 14 Day1 B 7.01711
3 15 Day1 B 6.200715
4 16 Day1 B 6.613928
5 17 Day1 A 6.829968
6 18 Day1 A 7.387583
7 19 Day1 A 7.367293
8 20 Day1 A 8.018853
9 21 Day1 C 7.527408
10 22 Day1 C 6.746739
11 23 Day1 C 7.29691
12 24 Day1 C 6.98336
13 29 Day1 B 6.816621
14 30 Day1 B 6.571689
15 31 Day1 B 5.911261
16 32 Day1 B 6.954988
17 33 Day1 C 7.624122
18 34 Day1 C 7.669865
19 35 Day1 C 7.676225
20 36 Day1 C 7.263593
21 37 Day1 A 7.704737
22 38 Day1 A 7.328716
23 39 Day1 A 7.29561
24 40 Day1 A 5.96418
25 62 Day1 A 6.880814
26 63 Day1 A 6.926342
27 64 Day1 A 6.926342
28 65 Day1 A 7.562293
29 13 Day3 B 6.677607
30 14 Day3 B 7.023526
31 15 Day3 B 6.441864
32 16 Day3 B 7.020875
33 17 Day3 A 7.478931
34 18 Day3 A 7.495336
35 19 Day3 A 7.427709
36 20 Day3 A 7.63302
37 21 Day3 C 7.382091
38 22 Day3 C 7.359731
39 23 Day3 C 7.285889
40 24 Day3 C 7.496863
41 29 Day3 B 6.632403
42 30 Day3 B 6.171196
43 31 Day3 B 6.306012
44 32 Day3 B 7.253833
45 33 Day3 C 7.594852
46 34 Day3 C 6.915225
47 35 Day3 C 7.220147
48 36 Day3 C 7.298227
49 37 Day3 A 7.573612
50 38 Day3 A 7.36655
51 39 Day3 A 7.560513
52 40 Day3 A 7.289078
53 62 Day3 A 7.287802
54 63 Day3 A 7.155336
55 64 Day3 A 7.394452
56 65 Day3 A 7.465383
57 13 Day6 B 6.976048
58 14 Day6 B 7.222966
59 15 Day6 B 6.584153
60 16 Day6 B 7.013223
61 17 Day6 A 7.569905
62 18 Day6 A 7.459185
63 19 Day6 A 7.504068
64 20 Day6 A 7.801867
65 21 Day6 C 7.598728
66 22 Day6 C 7.475841
67 23 Day6 C 7.511873
68 24 Day6 C 7.518384
69 29 Day6 B 6.618589
70 30 Day6 B 5.854754
71 31 Day6 B 6.125749
72 32 Day6 B 6.96272
73 33 Day6 C 7.5406
74 34 Day6 C 7.379861
75 35 Day6 C 7.344189
76 36 Day6 C 7.362815
77 37 Day6 A 7.805802
78 38 Day6 A 7.764172
79 39 Day6 A 7.789844
80 40 Day6 A 7.616437
81 62 Day6 A NA
82 63 Day6 A NA
83 64 Day6 A NA
84 65 Day6 A NA

....


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