Random effects, glmer, nested design - statistics

I have the following question:
I am analyzing the number of seed capsules between different genotypes (A,B and C)
I have 4 replicates for each genotype and in each of these replicates, I have 8 plants. Here is an example of the data:
Genotype Replicate_ID Plant_ID Seed_capsules
A 1 1 6
A 1 2 10
A 1 3 15
B 2 1 100
B 2 2 40
B 2 3 63
C 3 1 80
C 3 2 90
C 3 3 100
I used the glmer on the data but I am not sure whether my random is the replicate_ID or the plant_ID or both. Here is an example of what I tried so far:
freplicate_ID <- factor(newdata$replicate_ID)
fplant_ID <- factor(newdata$plant_ID)
m5 <- glmer(seed_capsules ~ pop_ID + (1| freplicate_ID /fplant_ID), family=poisson,data = data)
Further, How do I obtain the diagnostic plots for such a model? How do I compare between the genotypes? Do I need to run lsmeans on the model? Like this for example:
lsmeans(m5,pairwise ~ pop_ID, data=newdata) .
I thank you in advance for your help.
best,
Anna

Related

Is there a way to sort a list so that rows with the same value in one column are evenly distributed?

Hoping to sort (below left) by sector but distribute evenly (below right):
Name
Sector.
Name.
Sector
A
1
A
1
B
1
E
2
C
1
H
3
D
4
D
4
E
2
B
1
F
2
F
2
G
2
J
3
H
3
I
4
I
4
C
1
J
3
G
2
Real data is 70+ rows with 4 sectors.
I've worked around it manually but would love to figure out how to do it with a formula in excel.
Here's a more complete (and hopefully more accurate) idea - the carouselOrder is the column I'd like to generate via a formula.
guestID
guestSector
carouselOrder
1
1
1
2
1
5
3
1
9
4
1
13
5
2
2
6
2
6
7
2
10
8
2
14
9
3
3
10
3
7
11
3
11
12
2
18
13
1
17
14
1
20
15
1
23
16
2
21
17
2
24
18
2
27
19
1
26
20
1
29
21
1
30
22
1
31
23
3
15
24
3
19
25
3
22
26
3
25
27
3
28
28
1
32
29
4
4
30
4
8
31
4
12
32
4
16
When using Office 365 you can use the following in D2: =MOD(SEQUENCE(COUNTA(A2:A11),,0),4)+1
This create the repetitive counter of the sectors 1 to 4 to the total count of rows in your data.
In C2 use the following:
=BYROW(D2#,LAMBDA(x,
INDEX(
FILTER($A$2:$A$11,$B$2:$B$11=x),
SUM(--(D$2:x=x)))))
This filters the Names that equal the sector of mentioned row and indexes it to show only the result where the row in the filter result equals the count of the same sector (D2#) up to current row.
Let's try the following approach that doesn't require to create a helper column. I would like to explain first the logic to build the recurrence, then the excel formula that builds such recurrence.
If we sort the input data Name and Sector. by Sector. in ascending order, the new positions of the Name values (letters) can be calculated as follow (Table 1):
Name
Sector.Sorted
Position
A
1
1+4*0=1
B
1
1+4*1=5
C
1
1+4*2=9
E
2
2+4*0=2
F
2
2+4*1=6
G
2
2*4*2=10
H
3
3+4*0=3
J
3
3+4*1=7
D
4
4+4*0=4
I
4
4+4*1=8
The new positions of Name (letters) follows this pattern (Formula 1):
position = Sector.Sorted + groupSize * factor
where groupSize is 4 in our case and factor counts how many times the same Sector.Sorted value is repeated, starting from 0. Think about Sector.Sorted as groups, where each set of repeated values represents a group: 1,2,3 and 4.
If we are able to build the Position values we can sort Name, based on the new positions via SORTBY(array, by_array1) function. Check SORTBY documentation for more information how this function works.
Here is the formula to get the Name sorted in cell E2:
=LET(groupSize, 4, sorted, SORT(A2:B11,2), sName,
INDEX(sorted,,1),sSector, INDEX(sorted,,2),
seq0, SEQUENCE(ROWS(sSector),,0), mapResult,
MAP(sSector, seq0, LAMBDA(a,b, IF(b=0, "SAME",
IF(a=INDEX(sSector,b), "SAME", "NEW")))), factor,
SCAN(-1,mapResult, LAMBDA(aa,c,IF(c="SAME", aa+1,0))),
pos,MAP(sSector, factor, LAMBDA(m,n, m + groupSize*n)),
SORTBY(sName,pos)
)
Here is the output:
Explanation
The name sorted represents the input data sorted by Sector. in ascending order, i.e.: SORT(A2:B11,2). The names sName and sSector represent each column of sorted.
To identify each group we need the following sequence (seq0) starting from 0, i.e. SEQUENCE(ROWS(sSector),,0).
Now we need to identify when a new group starts. We use MAP function for that and the result is represented by the name mapResult:
MAP(sSector, seq0, LAMBDA(a,b, IF(b=0, "SAME",
IF(a=INDEX(sSector,b), "SAME", "NEW"))))
The logic is the following: If we are at the beginning of the sequence (first value of seq0), then returns SAME otherwise we check current value of sSector (a) against the previous one represented by INDEX(sSector,b) if they are the same, then we are in the same group, otherwise a new group started.
The intermediate result of mapResult is:
Name
Sector Sorted
mapResult
A
1
SAME
B
1
SAME
C
1
SAME
E
2
NEW
F
2
SAME
G
2
SAME
H
3
NEW
J
3
SAME
D
4
NEW
I
4
SAME
The first two columns are shown just for illustrative purpose, but mapResult only returns the last column.
Now we just need to create the counter based on every time we find NEW. In order to do that we use SCAN function and the result is stored under the name factor. This value represents the factor we use to multiply by 4 within each group (see Table 1):
SCAN(-1,mapResult, LAMBDA(aa,c,IF(c="SAME", aa+1,0)))
The accumulator starts in -1, because the counter starts with 0. Every time we find SAME, it increments by 1 the previous value. When it finds NEW (not equal to SAME), the accumulator is reset to 0.
Here is the intermediate result of factor:
Name
Sector Sorted
mapResult
factor
A
1
SAME
0
B
1
SAME
1
C
1
SAME
2
E
2
NEW
0
F
2
SAME
1
G
2
SAME
2
H
3
NEW
0
J
3
SAME
1
D
4
NEW
0
I
4
SAME
1
The first three columns are shown for illustrative purpose.
Now we have all the elements to build our pattern for the new positions represented with the name pos:
MAP(sSector, factor, LAMBDA(m,n, m + groupSize*n))
where m represents each element of Sector.Sorted and factor the previous calculated values. As you can see the formula in Excel represents the generic formula (Formula 1 see above). The intermediate result will be:
Name
Sector Sorted
mapResult
factor
pos
A
1
SAME
0
1
B
1
SAME
1
5
C
1
SAME
2
9
E
2
NEW
0
2
F
2
SAME
1
6
G
2
SAME
2
10
H
3
NEW
0
3
J
3
SAME
1
7
D
4
NEW
0
4
I
4
SAME
1
8
The previous columns are shown just for illustrative purpose. Now we have the new positions, so we are ready to sort based on the new positions for Name via:
SORTBY(sName,pos)
Update
The first MAP can be removed creating an array as input for SCAN that has the information of sSector and the index position to be used for finding the previous element. SCAN only allows a single array as input argument, so we can combine both information in a new array. This is the formula can be used instead:
=LET(groupSize, 4, sorted, SORT(A2:B11,2), sName,
INDEX(sorted,,1),sSector, INDEX(sorted,,2),
factor, SCAN(-1,sSector&"-"&SEQUENCE(ROWS(sSector),,0),
LAMBDA(aa,b, LET(s, TEXTSPLIT(b,"-"),item, INDEX(s,,1),
idx, INDEX(s,,2), IF(aa=-1, 0, IF(1*item=INDEX(sSector, idx), aa+1,0))))),
pos,MAP(sSector, factor, LAMBDA(m,n, m + groupSize*n)),
SORTBY(sName,pos)
)
We use inside of SCAN a LET function to calculate all required elements for doing the comparison as part of the calculation of the corresponding LAMBDA function. We extract the item and the idx position used to find previous element of sSector via:
1*item=INDEX(sSector, idx)
we are able to compare each element of sSector with previous one, starting from the second element of sSector. We multiply item by 1, because TEXTSPLIT converts the result to text, otherwise the comparison will fail.

pandas groupby extract top percent n data(descending)

I have some data like this
df = pd.DataFrame({'class':['a','a','b','b','a','a','b','c','c'],'score':[3,5,6,7,8,9,10,11,14]})
df
class score
0 a 3
1 a 5
2 b 6
3 b 7
4 a 8
5 a 9
6 b 10
7 c 11
8 c 14
I want to use groupby function extract top n% data(descending by score),i know the nlargest can make it,but the number of every group is different,so i don't know how to do it
I tried this function
top_n = 0.5
g = df.groupby(['class'])['score'].apply(lambda x:x.nlargest(int(round(top_n*len(x))),keep='all')).reset_index()
g
class level_1 score
0 a 5 9
1 a 4 8
2 b 6 10
3 b 3 7
4 c 8 14
but it can not deal with big data(more than 10 million),it is very slow,how do i speed it,thank you!

Combining the respective columns from 2 separate DataFrames using pandas

I have 2 large DataFrames with the same set of columns but different values. I need to combine the values in respective columns (A and B here, maybe be more in actual data) into single values in the same columns (see required output below). I have a quick way of implementing this using np.vectorize and df.to_numpy() but I am looking for a way to implement this strictly with pandas. Criteria here is first readability of code then time complexity.
df1 = pd.DataFrame({'A':[1,2,3,4,5], 'B':[5,4,3,2,1]})
print(df1)
A B
0 1 5
1 2 4
2 3 3
3 4 2
4 5 1
and,
df2 = pd.DataFrame({'A':[10,20,30,40,50], 'B':[50,40,30,20,10]})
print(df2)
A B
0 10 50
1 20 40
2 30 30
3 40 20
4 50 10
I have one way of doing it which is quite fast -
#This function might change into something more complex
def conc(a,b):
return str(a)+'_'+str(b)
conc_v = np.vectorize(conc)
required = pd.DataFrame(conc_v(df1.to_numpy(), df2.to_numpy()), columns=df1.columns)
print(required)
#Required Output
A B
0 1_10 5_50
1 2_20 4_40
2 3_30 3_30
3 4_40 2_20
4 5_50 1_10
Looking for an alternate way (strictly pandas) of solving this.
Criteria here is first readability of code
Another simple way is using add and radd
df1.astype(str).add(df2.astype(str).radd('-'))
A B
0 1-10 5-50
1 2-20 4-40
2 3-30 3-30
3 4-40 2-20
4 5-50 1-10

Is there a way to hide the same values in MultiIndex level 1?

I have the following dataframe (named test) in pandas:
Group 1 Group 2 Species Adj. P-value
0 a b Parabacteroides goldsteinii 7
1 a b Parabacteroides johnsonii 8
2 a b Parabacteroides merdae 9
3 a b Parabacteroides sp 10
4 c d Bacteroides coprocola 1
5 c d Bacteroides dorei 2
I would like to transform this table in latex format, but with the repeated values in Group 1 and Group 2 centred (see figure below for an example). In latex this is done with the package \multirow, and df.to_latex has a parameter called multirow to enable this (to_latex)
However, a MultiIndex has to be created in order to use the multirow option in to_latex.
So I did this:
test.index = pd.MultiIndex.from_frame(test[["Group 1","Group 2"]])
test = test.drop(["Group 1","Group 2"], axis=1)
test
Species Adj. P-value
Group 1 Group 2
a b Parabacteroides goldsteinii 7
b Parabacteroides johnsonii 8
b Parabacteroides merdae 9
b Parabacteroides sp 10
c d Bacteroides coprocola 1
d Bacteroides dorei 2
And finally I stored the table:
test.to_latex("la_tex_tab.txt",multirow=True, index=True,float_format="{:0.3f}".format).
However, this yields:
It works just for level 0 (Group 1) but not for level 1 (Group 2) of the MultiIndex. Do you have any suggestions about how to avoid the repetitions of the values b and d in the MultiIndex?
Thank you.
Kind of a hack if you want:
test['Group 2'] = test['Group 2'].mask(test['Group 2'].duplicated(),'')
test.set_index(["Group 1","Group 2"])
Species Adj. P-value
Group 1 Group 2
a b Parabacteroides goldsteinii 7
Parabacteroides johnsonii 8
Parabacteroides merdae 9
Parabacteroides sp 10
c d Bacteroides coprocola 1
Bacteroides dorei 2
We can do it for display only by use assign with blank column
test = test.assign(help='').set_index('help',append=True).drop(["Group 1","Group 2"], axis=1)

pandas random shuffling dataframe with constraints

I have a dataframe that I need to randomise in a very specific way with a particular rule, and I'm a bit lost. A simplified version is here:
idx type time
1 a 1
2 a 1
3 a 1
4 b 2
5 b 2
6 b 2
7 a 3
8 a 3
9 a 3
10 b 4
11 b 4
12 b 4
13 a 5
14 a 5
15 a 5
16 b 6
17 b 6
18 b 6
19 a 7
20 a 7
21 a 7
If we consider this as containing seven "bunches", I'd like to randomly shuffle by those bunches, i.e. retaining the time column. However, the constraint is that after shuffling, a particular bunch type (a or b in this case) cannot appear more than n (e.g. 2) times in a row. So an example correct result looks like this:
idx type time
21 a 7
20 a 7
19 a 7
7 a 3
8 a 3
9 a 3
17 b 6
16 b 6
18 b 6
6 b 2
5 b 2
4 b 2
2 a 1
3 a 1
1 a 1
14 a 5
13 a 5
15 a 5
12 b 4
11 b 4
10 b 4
I was thinking I could create a separate "order" array from 1 to 7 and np.random.shuffle() it, then sort the dataframe by time in that order, which will probably work - I can think of ways to do that part, but I'm especially struggling with the rule of restricting the number of repeats.
I know roughly that I should use a while loop, shuffle it in that way, loop over the frame and track the number of consecutive types, if it exceeds my n then break out and start the while loop again until it completes without breaking out, in which case set a value to end the while loop. But this got so messy and didn't work.
Any ideas?
See if this works.
import pandas as pd
import numpy as np
n = [['a',1],['a',1],['a',1],
['b',2],['b',2],['b',2],
['a',3],['a',3],['a',3]]
df = pd.DataFrame(n)
df.columns = ['type','time']
print(df)
order = np.unique(np.array(df['time']))
print("Before Shuffling",order)
np.random.shuffle(order)
print("Shuffled",order)
n =2
for i in order:
print(df[df['time']==i].iloc[0:n])

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