using the search function did not help me to find a solution for my problem which is why I created this post.
First of all, I am fairly new to Python and therefore, my knowledge is limited.
I am analysing a data set, which is based on time use diaries. Thereby, the columns represent the time steps (tb1_1 - tb1_144) while the rows represent the respective individual who filled out the journal (more than 60k observations). Furthermore, the value in each cell represents the activity performed for each time step. (for instance, 1 = sleeping etc.) The dataset looks like this:
For my analysis, I want to create activity profiles based on the information given by the diary entries by using time-inhomogeneous Markov chains which, graphically will look like this:
I have already looked at numerous examples of how to calculate Markov chains in Python. However, none of these examples take into account that, for each time step t, new transition matrices need to be derived from the initial dataset.
I would be very happy if someone could help me with this.
Thanks, Felix
-----UPDATE---------
After a couple of tries, I finally figured out how to build dynamic matrices. Please find the code below. If anyone knows how to further shorten it, feel free to comment :)
# generate transition probability matrices
matrix_drei_personen_haus_winter_weekday_ft_master= np.empty(shape=(144, 14, 14))
def a1(x,y):
try:
return x/y
except ZeroDivisionError:
return 0
for i in range (0,144):
for j in range (1,15):
for m in range (1,15):
a=a1(len(drei_personen_haus_winter_weekday_ft_master[(drei_personen_haus_winter_weekday_ft_master.iloc[:,i]==j)&(drei_personen_haus_winter_weekday_ft_master.iloc[:,i+1]==m)]),len(drei_personen_haus_winter_weekday_ft_master[drei_personen_haus_winter_weekday_ft_master.iloc[:,i]==j]))
matrix_drei_personen_haus_winter_weekday_ft_master[i,j-1,m-1]=a
#create discrete heterogeneous Markov-chain
def activity_forecast(steps):
# Choose the starting state
activityToday = "4"
print("Start state: " + activityToday)
# Shall store the sequence of states taken. So, this only has the starting state for now.
activityList = [activityToday]
i = 0
while i != steps:
#create sequence of activities
if activityToday == "1":
change = np.random.choice(transitionName[0],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,0,:])
if change == "11":
activityList.append("1")
pass
elif change == "12":
activityToday = "2"
activityList.append("2")
elif change == "13":
activityToday = "3"
activityList.append("3")
elif change == "14":
activityToday = "4"
activityList.append("4")
elif change == "15":
activityToday = "5"
activityList.append("5")
elif change == "16":
activityToday = "6"
activityList.append("6")
elif change == "17":
activityToday = "7"
activityList.append("7")
elif change == "18":
activityToday = "8"
activityList.append("8")
elif change == "19":
activityToday = "9"
activityList.append("9")
elif change == "0110":
activityToday = "10"
activityList.append("10")
elif change == "0111":
activityToday = "11"
activityList.append("11")
elif change == "0112":
activityToday = "12"
activityList.append("12")
elif change == "0113":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "2":
change = np.random.choice(transitionName[1],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,1,:])
if change == "22":
activityList.append("2")
pass
elif change == "21":
activityToday = "1"
activityList.append("1")
elif change == "23":
activityToday = "3"
activityList.append("3")
elif change == "24":
activityToday = "4"
activityList.append("4")
elif change == "25":
activityToday = "5"
activityList.append("5")
elif change == "26":
activityToday = "6"
activityList.append("6")
elif change == "27":
activityToday = "7"
activityList.append("7")
elif change == "28":
activityToday = "8"
activityList.append("8")
elif change == "29":
activityToday = "9"
activityList.append("9")
elif change == "210":
activityToday = "10"
activityList.append("10")
elif change == "211":
activityToday = "11"
activityList.append("11")
elif change == "112":
activityToday = "12"
activityList.append("12")
elif change == "213":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "3":
change = np.random.choice(transitionName[2],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,2,:])
if change == "33":
activityList.append("3")
pass
elif change == "31":
activityToday = "1"
activityList.append("1")
elif change == "32":
activityToday = "2"
activityList.append("2")
elif change == "34":
activityToday = "4"
activityList.append("4")
elif change == "35":
activityToday = "5"
activityList.append("5")
elif change == "36":
activityToday = "6"
activityList.append("6")
elif change == "37":
activityToday = "7"
activityList.append("7")
elif change == "38":
activityToday = "8"
activityList.append("8")
elif change == "39":
activityToday = "9"
activityList.append("9")
elif change == "310":
activityToday = "10"
activityList.append("10")
elif change == "311":
activityToday = "11"
activityList.append("11")
elif change == "312":
activityToday = "12"
activityList.append("12")
elif change == "313":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "4":
change = np.random.choice(transitionName[3],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,3,:])
if change == "44":
activityList.append("4")
pass
elif change == "42":
activityToday = "2"
activityList.append("2")
elif change == "43":
activityToday = "3"
activityList.append("3")
elif change == "41":
activityToday = "1"
activityList.append("1")
elif change == "45":
activityToday = "5"
activityList.append("5")
elif change == "46":
activityToday = "6"
activityList.append("6")
elif change == "47":
activityToday = "7"
activityList.append("7")
elif change == "48":
activityToday = "8"
activityList.append("8")
elif change == "49":
activityToday = "9"
activityList.append("9")
elif change == "310":
activityToday = "10"
activityList.append("10")
elif change == "411":
activityToday = "11"
activityList.append("11")
elif change == "412":
activityToday = "12"
activityList.append("12")
elif change == "413":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "5":
change = np.random.choice(transitionName[4],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,4,:])
if change == "55":
activityList.append("5")
pass
elif change == "52":
activityToday = "2"
activityList.append("2")
elif change == "53":
activityToday = "3"
activityList.append("3")
elif change == "54":
activityToday = "4"
activityList.append("4")
elif change == "51":
activityToday = "1"
activityList.append("1")
elif change == "56":
activityToday = "6"
activityList.append("6")
elif change == "57":
activityToday = "7"
activityList.append("7")
elif change == "58":
activityToday = "8"
activityList.append("8")
elif change == "59":
activityToday = "9"
activityList.append("9")
elif change == "510":
activityToday = "10"
activityList.append("10")
elif change == "511":
activityToday = "11"
activityList.append("11")
elif change == "512":
activityToday = "12"
activityList.append("12")
elif change == "513":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "6":
change = np.random.choice(transitionName[5],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,5,:])
if change == "66":
activityList.append("6")
pass
elif change == "62":
activityToday = "2"
activityList.append("2")
elif change == "63":
activityToday = "3"
activityList.append("3")
elif change == "64":
activityToday = "4"
activityList.append("4")
elif change == "65":
activityToday = "5"
activityList.append("5")
elif change == "61":
activityToday = "1"
activityList.append("1")
elif change == "67":
activityToday = "7"
activityList.append("7")
elif change == "68":
activityToday = "8"
activityList.append("8")
elif change == "69":
activityToday = "9"
activityList.append("9")
elif change == "610":
activityToday = "10"
activityList.append("10")
elif change == "611":
activityToday = "11"
activityList.append("11")
elif change == "612":
activityToday = "12"
activityList.append("12")
elif change == "613":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "7":
change = np.random.choice(transitionName[6],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,6,:])
if change == "77":
activityList.append("7")
pass
elif change == "72":
activityToday = "2"
activityList.append("2")
elif change == "73":
activityToday = "3"
activityList.append("3")
elif change == "74":
activityToday = "4"
activityList.append("4")
elif change == "75":
activityToday = "5"
activityList.append("5")
elif change == "76":
activityToday = "6"
activityList.append("6")
elif change == "71":
activityToday = "1"
activityList.append("1")
elif change == "78":
activityToday = "8"
activityList.append("8")
elif change == "79":
activityToday = "9"
activityList.append("9")
elif change == "710":
activityToday = "10"
activityList.append("10")
elif change == "711":
activityToday = "11"
activityList.append("11")
elif change == "712":
activityToday = "12"
activityList.append("12")
elif change == "713":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "8":
change = np.random.choice(transitionName[7],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,7,:])
if change == "88":
activityList.append("8")
pass
elif change == "82":
activityToday = "2"
activityList.append("2")
elif change == "83":
activityToday = "3"
activityList.append("3")
elif change == "84":
activityToday = "4"
activityList.append("4")
elif change == "85":
activityToday = "5"
activityList.append("5")
elif change == "86":
activityToday = "6"
activityList.append("6")
elif change == "87":
activityToday = "7"
activityList.append("7")
elif change == "81":
activityToday = "1"
activityList.append("1")
elif change == "89":
activityToday = "9"
activityList.append("9")
elif change == "810":
activityToday = "10"
activityList.append("10")
elif change == "811":
activityToday = "11"
activityList.append("11")
elif change == "812":
activityToday = "12"
activityList.append("12")
elif change == "813":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "9":
change = np.random.choice(transitionName[8],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,8,:])
if change == "99":
activityList.append("9")
pass
elif change == "92":
activityToday = "2"
activityList.append("2")
elif change == "93":
activityToday = "3"
activityList.append("3")
elif change == "94":
activityToday = "4"
activityList.append("4")
elif change == "95":
activityToday = "5"
activityList.append("5")
elif change == "96":
activityToday = "6"
activityList.append("6")
elif change == "97":
activityToday = "7"
activityList.append("7")
elif change == "98":
activityToday = "8"
activityList.append("8")
elif change == "91":
activityToday = "1"
activityList.append("1")
elif change == "910":
activityToday = "10"
activityList.append("10")
elif change == "911":
activityToday = "11"
activityList.append("11")
elif change == "912":
activityToday = "12"
activityList.append("12")
elif change == "913":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "10":
change = np.random.choice(transitionName[9],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,9,:])
if change == "1010":
activityList.append("10")
pass
elif change == "102":
activityToday = "2"
activityList.append("2")
elif change == "103":
activityToday = "3"
activityList.append("3")
elif change == "104":
activityToday = "4"
activityList.append("4")
elif change == "105":
activityToday = "5"
activityList.append("5")
elif change == "106":
activityToday = "6"
activityList.append("6")
elif change == "107":
activityToday = "7"
activityList.append("7")
elif change == "108":
activityToday = "8"
activityList.append("8")
elif change == "109":
activityToday = "9"
activityList.append("9")
elif change == "101":
activityToday = "1"
activityList.append("1")
elif change == "1011":
activityToday = "11"
activityList.append("11")
elif change == "1012":
activityToday = "12"
activityList.append("12")
elif change == "1013":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "11":
change = np.random.choice(transitionName[10],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,10,:])
if change == "1111":
activityList.append("11")
pass
elif change == "112":
activityToday = "2"
activityList.append("2")
elif change == "113":
activityToday = "3"
activityList.append("3")
elif change == "114":
activityToday = "4"
activityList.append("4")
elif change == "115":
activityToday = "5"
activityList.append("5")
elif change == "116":
activityToday = "6"
activityList.append("6")
elif change == "117":
activityToday = "7"
activityList.append("7")
elif change == "118":
activityToday = "8"
activityList.append("8")
elif change == "119":
activityToday = "9"
activityList.append("9")
elif change == "1110":
activityToday = "10"
activityList.append("10")
elif change == "111":
activityToday = "1"
activityList.append("1")
elif change == "1112":
activityToday = "12"
activityList.append("12")
elif change == "1113":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "12":
change = np.random.choice(transitionName[11],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,11,:])
if change == "1212":
activityList.append("12")
pass
elif change == "122":
activityToday = "2"
activityList.append("2")
elif change == "123":
activityToday = "3"
activityList.append("3")
elif change == "124":
activityToday = "4"
activityList.append("4")
elif change == "125":
activityToday = "5"
activityList.append("5")
elif change == "126":
activityToday = "6"
activityList.append("6")
elif change == "127":
activityToday = "7"
activityList.append("7")
elif change == "128":
activityToday = "8"
activityList.append("8")
elif change == "129":
activityToday = "9"
activityList.append("9")
elif change == "1210":
activityToday = "10"
activityList.append("10")
elif change == "1211":
activityToday = "11"
activityList.append("11")
elif change == "121":
activityToday = "1"
activityList.append("1")
elif change == "1213":
activityToday = "13"
activityList.append("13")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "13":
change = np.random.choice(transitionName[12],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,12,:])
if change == "1313":
activityList.append("13")
pass
elif change == "132":
activityToday = "2"
activityList.append("2")
elif change == "133":
activityToday = "3"
activityList.append("3")
elif change == "134":
activityToday = "4"
activityList.append("4")
elif change == "135":
activityToday = "5"
activityList.append("5")
elif change == "136":
activityToday = "6"
activityList.append("6")
elif change == "137":
activityToday = "7"
activityList.append("7")
elif change == "138":
activityToday = "8"
activityList.append("8")
elif change == "139":
activityToday = "9"
activityList.append("9")
elif change == "1310":
activityToday = "10"
activityList.append("10")
elif change == "1311":
activityToday = "11"
activityList.append("11")
elif change == "1312":
activityToday = "12"
activityList.append("12")
elif change == "131":
activityToday = "1"
activityList.append("1")
else:
activityToday = "14"
activityList.append("14")
elif activityToday == "14":
change = np.random.choice(transitionName[13],replace=True,p=matrix_drei_personen_haus_winter_weekday_ft_master[i,13,:])
if change == "1414":
activityList.append("14")
pass
elif change == "142":
activityToday = "2"
activityList.append("2")
elif change == "143":
activityToday = "3"
activityList.append("3")
elif change == "144":
activityToday = "4"
activityList.append("4")
elif change == "145":
activityToday = "5"
activityList.append("5")
elif change == "146":
activityToday = "6"
activityList.append("6")
elif change == "147":
activityToday = "7"
activityList.append("7")
elif change == "148":
activityToday = "8"
activityList.append("8")
elif change == "149":
activityToday = "9"
activityList.append("9")
elif change == "1410":
activityToday = "10"
activityList.append("10")
elif change == "1411":
activityToday = "11"
activityList.append("11")
elif change == "1412":
activityToday = "12"
activityList.append("12")
elif change == "1413":
activityToday = "13"
activityList.append("13")
else:
activityToday = "1"
activityList.append("1")
i += 1
print("Possible states: " + str(activityList))
print("End state after "+ str(steps) + " steps: " + activityToday)
# Function that forecasts the possible state for the next 144 steps
activity_forecast(143)
