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How to calculate FactorAnalysis scores using Python (scikit-learn)?
Asked Answered
Solved pythonrscikit-learnfactor-analysis
W

2

8

I need to perform exploratory factor analysis and calculate scores for each observation using Python assuming that there is only 1 underlying factor. It seems that sklearn.decomposition.FactorAnalysis() is the way to go, but unfortunately documentation and example (unfortunately I was unable to find other examples) are not clear enough for me to figure out how to get the job done.

I have following test file with 41 observations of 29 variables (test.csv):

49.6,34917,24325.4,305,101350,98678,254.8,276.9,47.5,1,3,5.6,3.59,11.9,0,97.5,97.6,8,10,100,0,0,96.93,610.1,100,1718.22,6.7,28,5
275.8,14667,11114.4,775,75002,74677,30,109,9.1,1,0,6.5,3.01,8.2,1,97.5,97.6,8,8,100,0,0,100,1558,100,2063.17,5.5,64,5
2.3,9372.5,8035.4,4.6,8111,8200,8.01,130,1.2,0,5,0,3.33,6.09,1,97.9,97.9,8,8,67.3,342.3,0,99.96,18.3,53,1457.27,4.8,8,4
7.10,13198.0,13266.4,1.1,708,695,6.1,80,0.4,0,4,0,3.1,8.2,1,97.8,97.9,8,8,45,82.7,0,99.68,4.5,80,1718.22,13.8,0,3
1.97,2466.7,2900.6,19.7,5358,5335,10.1,23,0.5,0,2,0,3.14,8.2,0,97.3,97.2,9,9,74.5,98.2,0,99.64,79.8,54,1367.89,6.4,12,4
2.40,2999.4,2218.2,0.80,2045,2100,8.9,10,1.5,1,3,0,2.82,8.6,0,97.4,97.2,8,8,47.2,323.8,0,99.996,13.6,24,1249.67,2.7,12,3
0.59,4120.8,5314.5,0.54,14680,13688,14.9,117,1.1,0,3,0,2.94,3.4,0,97.6,97.7,8,8,11.8,872.6,0,100,9.3,52,1251.67,14,14,2
0.72,2067.7,2364,3,367,298,7.2,60,2.5,0,12,0,2.97,10.5,0,97.5,97.6,8,8,74.7,186.8,0,99.13,12,57,1800.45,2.7,4,2
1.14,2751.9,3066.8,3.5,1429,1498,7.7,9,1.6,0,3,0,2.86,7.7,0,97.6,97.8,8,9,76.7,240.1,0,99.93,13.6,60,1259.97,15,8,3
1.29,4802.6,5026.1,2.7,7859,7789,6.5,45,1.9,0,3,0,2.5,8.2,0,98,98,8,8,34,297.5,0,99.95,10,30,1306.44,8.5,0,4
0.40,639.0,660.3,1.3,23,25,1.5,9,0.1,0,1,0,2.5,8.2,0,97.7,97.8,8,8,94.2,0,0,100,4.3,50,1565.44,19.2,0,4
0.26,430.7,608.1,2,33,28,2.5,7,0.4,0,6,0,2.5,8.2,0,97.4,97.4,8,8,76.5,0,0,98.31,8,54,1490.08,0,0,4
4.99,2141.2,2357.6,3.60,339,320,8.1,7,0.2,0,8,0,2.5,5.9,0,97.3,97.4,8,8,58.1,206.3,0,99.58,13.2,95,1122.92,14.2,8,2
0.36,1453.7,1362.2,3.50,796,785,3.7,9,0.1,0,9,0,2.5,13.6,0,98,98.1,8,8,91.4,214.6,0,99.74,7.5,53,1751.98,11.5,0,2
0.36,1657.5,2421.1,2.8,722,690,8.1,8,0.4,0,1,0,2.5,8.2,0,97.2,97.3,11,12,37.4,404.2,0,99.98,10.9,35,1772.33,10.2,8,3
1.14,5635.2,5649.6,3,2681,2530,5.4,20,0.3,0,1,0,3.1,8.2,0,97.7,97.8,8,11,50.1,384.7,0,99.02,11.6,27,1306.08,16,0,2
0.6,1055.9,1487.9,1.3,69,65,2.5,6,0.4,0,8,0,2.5,8.2,0,97.9,97.7,8,11,63,137.9,0,99.98,5.1,48,1595.06,0,0,4
0.08,795.3,1174.7,1.40,85,76,2.2,7,0.2,0,0,0,2.5,8.2,0,97.4,97.5,8,8,39.3,149.3,0,98.27,5.1,52,1903.9,8.1,0,2
0.90,2514.0,2644.4,2.6,1173,1104,5.5,43,0.8,0,10,0,2.5,13.6,0,97.5,97.5,8,10,58.7,170.5,0,80.29,10,34,1292.72,4,0,2
0.27,870.4,949.7,1.8,252,240,2.2,31,0.2,0,1,0,2.5,8.2,0,97.5,97.6,8,8,64.5,0,0,100,6.6,29,1483.18,9.1,0,3
0.41,1295.1,2052.3,2.60,2248,2135,6.0,12,0.8,0,4,0,2.7,8.2,0,97.7,97.7,8,8,71.1,261.3,0,91.86,4.6,21,1221.71,9.4,0,4
1.10,3544.2,4268.9,2.1,735,730,6.6,10,1.7,0,14,0,2.5,8.2,0,97.7,97.8,8,8,52,317.2,0,99.62,9.8,46,1271.63,14.2,0,3
0.22,899.3,888.2,1.80,220,218,3.6,7,0.5,0,1,0,2.5,8.2,0,97.2,97.5,8,8,22.5,0,0,70.79,10.6,32,1508.02,0,0,4
0.24,1712.8,1735.5,1.30,41,35,5.4,7,0.5,0,1,0,3.28,8.2,0,97.8,97.8,9,10,16.6,720.2,0,99.98,4.3,53,1324.46,0,4,2
0.2,558.4,631.9,1.7,65,64,2.5,7,0.2,0,5,0,2.5,8.2,0,97.7,97.5,8,8,60.7,0,0,99.38,6.1,52,1535.08,0,0,2
0.21,599.9,1029,1.1,69,70,3.7,85.7,0.1,0,12,0,2.5,8.2,0,97.4,97.5,8,8,48.6,221.2,0,100,5.4,40,1381.44,25.6,0,2
0.10,131.3,190.6,1.6,28,25,2.9,7,0.3,0,3,0,2.5,8.2,0,97.7,97.8,8,8,58.9,189.4,0,99.93,6.9,42,1525.58,17.4,0,3
0.44,3881.4,5067.3,0.9,2732,2500,11.2,10,1.5,0,5,0,2.67,8.2,0,97.4,97.3,8,11,14.5,1326.2,0,99.06,3.7,31,1120.54,10.3,10,2
0.18,1024.8,1651.3,1.01,358,345,4.6,35,0.3,0,2,0,2.5,8.2,0,97.8,97.9,8,10,15.9,790.2,0,100,4.3,48,1531.04,10.5,0,3
0.46,682.9,784.2,1.8,103,109,2.2,8,0.4,0,4,0,2.5,8.2,0,97.8,97.9,8,8,82.7,166.3,0,99.96,6.4,44,1373.6,13.5,0,2
0.12,370.4,420.0,1.10,28,25,3.4,10,0.1,0,6,0,2.57,8.2,0,97.6,97.8,8,11,51.6,120,0,99.85,8.1,40,1297.94,0,0,3
0.03,552.4,555.1,0.8,54,49,3.5,10,0.4,0,0,0,2.5,8.2,0,97.4,97.6,8,10,33.6,594.5,0,100,3.2,41,1184.34,6.6,0,3
0.21,1256.5,2434.8,0.9,1265,1138,6.3,20,1.3,0,2,0,2.6,8.2,0,98,97.9,8,9,20.1,881,0,99.1,3.9,31,1265.93,7.8,0,3
0.09,320.6,745.7,1.10,37,25,2.7,8,0.3,0,9,0,2.5,8.2,0,98,97.8,8,8,49.2,376.4,0,99.95,4.3,39,1285.11,0,0,3
0.08,452.7,570.9,1,18,20,4.7,9,0.6,0,2,0,2.45,8.2,0,97.1,97.1,8,8,19.9,1103.8,0,99.996,2.9,22,1562.61,21.9,0,3
0.13,967.9,947.2,1,74,65,4.0,25,1.4,0,6,0,2.5,8.2,0,98,98,9,11,30.1,503.1,0,99.999,3.4,55,1269.33,0,0,2
0.07,495.0,570.3,1.2,27,30,4.3,7,0.5,0,12,0,3.62,8.2,0,98.2,98.2,15,13,29.8,430.5,0,99.7,4.9,40,1461.79,14.6,0,2
0.17,681.9,537.4,1.1,113,120,2.9,12,0.4,0,8,0,2.5,8.2,0,98.2,98.3,8,8,24,74.3,0,100,5,43,1290.16,0,0,3
0.05,639.7,898.2,0.40,9,12,3.0,7,0.1,0,1,0,2.5,8.2,0,97.6,97.8,15,11,11.9,1221.1,0,99.996,1.7,40,1372,7,0,4
0.65,2067.8,2084.2,2.50,414,398,7.3,6,0.7,0,4,0,2.16,8.2,0,97.8,97.9,12,12,60.1,146.3,0,99.96,10.4,44,1059.68,7.4,0,2
0.12,804.4,1416.4,3.30,579,602,4.2,7,1.8,0,1,0,2.5,8.2,0,98.1,98.3,8,10,8.9,2492.3,0,95.4,2.2,34,1345.76,7,0,2

Using the code I wrote based on the official example and from this post I get weird result. Code:

from sklearn import decomposition, preprocessing
from sklearn.cross_validation import cross_val_score
import csv
import numpy as np

data = np.genfromtxt('test.csv', delimiter=',')

def compute_scores(X):
    n_components = np.arange(0, len(X), 1)
    X = preprocessing.scale(X) # data normalisation attempt
    pca = decomposition.PCA()
    fa = decomposition.FactorAnalysis(n_components=1)

    pca_scores, fa_scores = [], []
    for n in n_components:
        pca.n_components = n
        fa.n_components = n
        #pca_scores.append(np.mean(cross_val_score(pca, X))) # if I attempt to compute pca_scores I get the error.
        fa_scores.append(np.mean(cross_val_score(fa, X)))

    print pca_scores, fa_scores
compute_scores(data)

Code output:

[],
 [-947738125363.77405,
  -947738145459.86035,
  -947738159924.70471,
  -947738174662.89746,
  -947738206142.62854,
  -947738179314.44739,
  -947738220921.50684,
  -947738223447.3678,
  -947738277298.33545,
  -947738383772.58606,
  -947738415104.84912,
  -947738406361.44482,
  -947738394379.30359,
  -947738456528.69275,
  -947738501001.14319,
  -947738991338.98291,
  -947739381280.06506,
  -947739389033.33557,
  -947739434992.48047,
  -947739549511.2655,
  -947739355699.70959,
  -947739879828.51514,
  -947739898216.39099,
  -947739905804.71033,
  -947739902618.47791,
  -947738564594.54639,
  -948816122907.87366,
  -947744046601.55029,
  -947738624937.61292,
  -947738625325.73486,
  -947738626111.14441,
  -947738624973.92188,
  -947738625200.06946,
  -947738625568.65027,
  -947738625528.69666,
  -947738625359.41992,
  -947738624906.67529,
  -947738625652.12439,
  -947739509002.01868,
  -947738625426.81946,
  -947738625380.45837]

This result is far from what is expected. Here is the R code for this task and the same data. It's output is OK (the result is close to the output from some IBM program that is able to perform FA):

data <-read.csv("test.csv", header=F)
col_names <- names(data)
drops <- c()

for (name in col_names){
  st_dev <- sd(data[,name], na.rm = T)
  if (st_dev == 0){
    drops <- c(drops, name)
  }
}

da_nal <- data[,!(names(data) %in% drops)]
factanal(na.omit(da_nal), factors = 1, scores = 'regression')$scores

The output for this code is:

    Factor1
1   4.89102190
2   3.65004187
3   0.14628700
4  -0.20255897
5  -0.01565570
6  -0.16438863
7   0.40835986
8  -0.25823984
9  -0.20813064
10  0.09390067
11 -0.28891296
12 -0.28882753
13 -0.26624358
14 -0.25202275
15 -0.25181326
16 -0.15653679
17 -0.28702281
18 -0.28865654
19 -0.23251509
20 -0.28066125
21 -0.18714387
22 -0.24969113
23 -0.28302552
24 -0.28712610
25 -0.29196529
26 -0.28659988
27 -0.29502523
28 -0.15802910
29 -0.27440118
30 -0.29083667
31 -0.29548220
32 -0.29461059
33 -0.23594859
34 -0.29654336
35 -0.29759659
36 -0.29085001
37 -0.29539071
38 -0.29234303
39 -0.29702103
40 -0.27595130
41 -0.27184361

So I'm looking to get the similar result in Python (I know that I won't get the exact numbers), but I don't know how.

Wolverhampton answered 28/7, 2015 at 15:23 Comment(2)
Just a comment - but I would be careful about interpreting results based on only 41 observations when using 29 variables for factor anlaysis. You should look up Meyer-Kaiser-Olkin tests to see if your data are suitable for factor analysis or not. – Loathing
@jalapic, yes I'm aware that I need at least twice as much observations as I have variables, but my client want it to be this way (I told him that the result will be misleading). – Wolverhampton
W
4

Seems that I figured out how to get scores.

from sklearn import decomposition, preprocessing
import numpy as np

data = np.genfromtxt('rangir_test.csv', delimiter=',')
data = data[~np.isnan(data).any(axis=1)]
data_normal = preprocessing.scale(data)
fa = decomposition.FactorAnalysis(n_components = 1)
fa.fit(data_normal)
for score in fa.score_samples(data_normal):
    print score

Unfortunately the output (see below) is very different to one from factanal(). Any advises on decomposition.FactorAnalysis() will be appreciated.

Scikit-learn scores output:

-69.8587183816
-116.353511148
-24.1529840248
-36.5366398005
-7.87165586175
-24.9012815104
-23.9148486368
-10.047780535
-4.03376369723
-7.07428842783
-7.44222705099
-6.25705487929
-13.2313513762
-13.3253819521
-9.23993173528
-7.141616656
-5.57915693405
-6.82400483045
-15.0906961724
-3.37447211233
-5.41032267015
-5.75224753811
-19.7230390792
-6.75268922909
-4.04911793705
-10.6062761691
-3.17417070498
-9.95916350005
-3.25893428094
-3.88566777358
-3.30908856716
-3.58141292341
-3.90778368669
-4.01462493538
-11.6683969455
-5.30068548445
-24.3400870389
-7.66035331181
-13.8321672858
-8.93461397086
-17.4068326999
Wolverhampton answered 11/8, 2015 at 11:7 Comment(2)
The problem that you are running into is that python is outputting the negative log-likelihood, whereas factanal outputs z-scores. – Thrash
This is an 3-year old question but I wanted to know if one can also get scores using command scores = fa.fit_transform(data_normal)? – Ruel
C
2

This is late but may be still interesting for OP or others who came here from google.

For everyone used to R factanal there is a python package available that wraps the R factanal function so that you can just call it from python with a pandas data frame like this:

from factanal.wrapper import factanal

fa_res = factanal(pdf, factors=4, scores='regression', rotation='promax', 
                  verbose=True, return_dict=True)

More information: https://pypi.org/project/factanal/

Install with:

pip install factanal
Cichocki answered 10/5, 2020 at 21:8 Comment(0)

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