System is computationally singular using mlogit in R

Question

I am conducting multinomial logistic regressions. They seem to work for all variables except for the price variable, where I get the following error:

reg.M <- mlogit::mlogit(formula = value ~ 1 | price, data = listDatasets[[2]])

Error in solve.default(H, g[!fixed]) : 
  system is computationally singular: reciprocal condition number = 7.4671e-18

That is my the head of the dataset used (I have 15 like these, with different prices):

> head(listDatasets[[2]])
             index Age ScoreEnvAtt MoneyInvested Gender Beliefs_eff_Green Beliefs_eff_ESG Beliefs_eff_Comp Beliefs_perf_ESG Beliefs_perf_Green Beliefs_perf_Comp Guilt Social.Altruistic Biospheric Egoistic DummyMedium
1.SS_Green_1     1  26         4.2            13      2                 4               3                3                2                  3                 2    71          6.000000   6.000000        5           1
1.SS_Green_2     1  26         4.2            13      2                 4               3                3                2                  3                 2    71          6.000000   6.000000        5           1
1.SS_Green_3     1  26         4.2            13      2                 4               3                3                2                  3                 2    71          6.000000   6.000000        5           1
1.SS_Green_4     1  26         4.2            13      2                 4               3                3                2                  3                 2    71          6.000000   6.000000        5           1
2.SS_Green_1     2  30         4.8             2      2                 4               3                4                2                  3                 3    26          6.666667   5.333333        5           1
2.SS_Green_2     2  30         4.8             2      2                 4               3                4                2                  3                 3    26          6.666667   5.333333        5           1
             DummyHigh CompensationGroup Past_compensation Knowledge_CO2   variable value price
1.SS_Green_1         0            Group1                 2             1 SS_Green_1 FALSE   1.5
1.SS_Green_2         0            Group1                 2             1 SS_Green_2 FALSE   1.5
1.SS_Green_3         0            Group1                 2             1 SS_Green_3 FALSE   1.5
1.SS_Green_4         0            Group1                 2             1 SS_Green_4  TRUE   1.3
2.SS_Green_1         0            Group2                 2             2 SS_Green_1 FALSE   1.5
2.SS_Green_2         0            Group2                 2             2 SS_Green_2 FALSE   1.5

I checked the other threads on this error already but can not find a solution to my problem. Any suggestions? Thanks!

Edit: I tried to do it with multinom instead of mlogit. It does not seem to recognize the levels of the dependent variable.

test <- multinom(value ~ price, listDatasets[[2]])

summary(test)

    > summary(test)
Call:
multinom(formula = value ~ price, data = listDatasets[[2]])

Coefficients:
               Values Std. Err.
(Intercept)  25.77925  1.464741
price       -18.86853  1.037180

Residual Deviance: 653.8391 
AIC: 657.8391

Edit 2:

dput(head(data_long))
structure(list(Pride = c(17, 71, 1, 50, 0, 13), Guilt = c(71, 
26, 89, 50, 100, 13), Shame = c(36, 77, 5, 50, 67, 8), Joy = c(12, 
50, 0, 50, 30, 37), Attitudes1 = c(6, 5, 7, 5, 7, 5), Attitudes2 = c(5, 
7, 3, 4, 5, 3), Attitudes3 = c(6, 6, 7, 6, 7, 6), Attitudes4 = c(5, 
3, 5, 5, 6, 6), Attitudes5 = c(4, 7, 6, 6, 5, 6), Attitudes6 = c(5, 
7, 3, 7, 7, 6), Attitudes7 = c(3, 4, 1, 3, 1, 6), Attitudes8 = c(3, 
4, 5, 6, 7, 2), Attitudes9 = c(2, 3, 7, 4, 7, 6), Attitudes10 = c(3, 
2, 5, 4, 7, 6), Concern1 = c(6, 4, 7, 6, 7, 6), Concern2 = c(6, 
6, 7, 6, 7, 6), Concern3 = c(5, 5, 7, 6, 4, 6), Concern4 = c(6, 
6, 5, 6, 4, 5), Concern5 = c(6, 7, 7, 6, 4, 5), Concern6 = c(6, 
6, 7, 6, 5, 6), Concern7 = c(6, 6, 7, 6, 7, 6), Concern8 = c(4, 
4, 5, 6, 3, 6), Concern9 = c(6, 7, 6, 6, 7, 7), Beliefs_perf_ESG = c(2, 
2, 3, 2, 3, 2), Beliefs_perf_Comp = c(2, 3, 2, 3, 3, 2), Beliefs_perf_Green = c(3, 
3, 3, NA, 3, 2), Beliefs_eff_ESG = c(3, 3, 4, 3, 4, 3), Beliefs_eff_Comp = c(3, 
4, 2, 4, 2, 3), Beliefs_eff_Green = c(4, 4, 5, 5, 5, 3), Eval_Ego = c(3, 
2, 3, 4, 2, 3), Eval_Nature1 = c(3, 3, 3, 4, 2, 2), Eval_Nature2 = c(4, 
4, 4, 4, 2, 3), Eval_Social = c(3, 2, 4, 4, 2, 3), Reforestation = c(2, 
1, 1, 2, 2, 3), Renewable_Energy = c(1, 2, 3, 1, 1, 1), Efficient_Energy = c(3, 
4, 4, 3, 3, 2), Methane = c(4, 3, 2, 4, 4, 4), France = c(3, 
3, 1, 1, 3, 2), Europe = c(2, 2, 3, 3, 2, 3), Development = c(1, 
1, 2, 2, 1, 1), Co_benefits = c(5, 4, 5, 3, 4, 4), Poverty = c(1, 
1, 2, 2, 1, 1), Health = c(4, 2, 4, 1, 3, 3), Biodiversity = c(2, 
4, 1, 3, 2, 2), Equality = c(3, 5, 5, 5, 5, 5), Economic_Growth = c(5, 
3, 3, 4, 4, 4), Knowledge_CO2 = c(1, 2, 3, 2, 2, 2), Past_compensation = c(2, 
2, 1, 2, 1, 2), Age = c(26, 30, 30, 30, 21, 40), Gender = c(2, 
2, 2, 2, 2, 2), MoneyInvested = c(13, 2, 1, 3, 13, 1), Investment_Experience = c(2, 
1, 1, 1, 2, 1), Participant_s_ID = c("1234asdf", "Password04", 
"hiquet8350", "masmas2121", "1712flju", "Lemurien4555"), Compensationproject1 = c(1, 
NA, NA, 1, NA, 1), Compensationproject2 = c(NA, 1, 1, NA, NA, 
NA), Compensationproject3 = c(NA, NA, NA, NA, 1, NA), FL_42_DO_ChoiceExperiment1 = c(6, 
14, 3, 13, 10, 7), FL_42_DO_ChoiceExperiment2 = c(3, 1, 4, 6, 
13, 2), FL_42_DO_ChoiceExperiment3 = c(7, 10, 1, 7, 11, 13), 
    FL_42_DO_ChoiceExperiment4 = c(11, 15, 5, 2, 4, 11), FL_42_DO_ChoiceExperiment5 = c(14, 
    7, 2, 11, 2, 10), FL_42_DO_ChoiceExperiment6 = c(2, 11, 8, 
    15, 5, 6), FL_42_DO_ChoiceExperiment7 = c(1, 6, 6, 12, 14, 
    1), FL_42_DO_ChoiceExperiment8 = c(10, 2, 14, 5, 9, 5), FL_42_DO_ChoiceExperiment9 = c(4, 
    8, 13, 1, 1, 8), FL_42_DO_ChoiceExperiment10 = c(12, 5, 7, 
    14, 6, 3), FL_42_DO_ChoiceExperiment11 = c(15, 13, 10, 10, 
    12, 14), FL_42_DO_ChoiceExperiment12 = c(13, 3, 12, 8, 7, 
    9), FL_42_DO_ChoiceExperiment13 = c(9, 9, 11, 9, 8, 15), 
    FL_42_DO_ChoiceExperiment14 = c(8, 12, 9, 3, 3, 12), FL_42_DO_ChoiceExperiment15 = c(5, 
    4, 15, 4, 15, 4), ScoreEnvAtt = c(4.2, 4.8, 4.9, 5, 5.9, 
    5.2), Eval_NatureScore = c(3.5, 3.5, 3.5, 4, 2, 2.5), Social.Altruistic = c(6, 
    6.66666666666667, 6, 6, 5, 5.66666666666667), Biospheric = c(6, 
    5.33333333333333, 7, 6, 7, 6), Egoistic = c(5, 5, 6.33333333333333, 
    6, 4, 6), GroupEnvAtt = structure(c(2L, 2L, 2L, 2L, 2L, 2L
    ), .Label = c("low", "medium", "high"), class = "factor"), 
    DummyMedium = structure(c(2L, 2L, 2L, 2L, 2L, 2L), .Label = c("0", 
    "1"), class = "factor"), CompensationGroup = structure(c(1L, 
    2L, 2L, 1L, 3L, 1L), .Label = c("Group1", "Group2", "Group3"
    ), class = "factor"), ID = structure(1:6, .Label = c("1", 
    "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", 
    "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", 
    "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", 
    "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", 
    "43", "44", "45", "46", "47", "48", "49", "50", "51", "52", 
    "53", "54", "55", "56", "57", "58", "59", "60", "61", "62", 
    "63", "64", "65", "66", "67", "68", "69", "70", "71", "72", 
    "73", "74", "75", "76", "77", "78", "79", "80", "81", "82", 
    "83", "84", "85", "86", "87", "88", "89", "90", "91", "92", 
    "93", "94", "95", "96", "97", "98", "99", "100", "101", "102", 
    "103", "104", "105", "106", "107", "108", "109", "110", "111", 
    "112", "113", "114", "115", "116", "117", "118", "119", "120", 
    "121", "122", "123", "124", "125", "126", "127", "128", "129", 
    "130", "131", "132", "133", "134", "135", "136", "137", "138", 
    "139", "140", "141", "142", "143", "144", "145", "146", "147", 
    "148", "149", "150", "151", "152", "153", "154", "155", "156", 
    "157", "158", "159", "160", "161", "162", "163", "164", "165", 
    "166", "167", "168", "169", "170", "171", "172", "173", "174", 
    "175", "176", "177", "178", "179", "180", "181", "182", "183", 
    "184", "185", "186", "187", "188", "189", "190", "191", "192", 
    "193", "194", "195", "196", "197", "198", "199", "200", "201", 
    "202", "203", "204", "205", "206", "207", "208", "209", "210", 
    "211", "212", "213", "214", "215", "216", "217", "218", "219", 
    "220", "221", "222", "223", "224", "225", "226", "227", "228", 
    "229", "230", "231", "232", "233", "234", "235", "236", "237", 
    "238", "239", "240", "241", "242", "243", "244", "245", "246", 
    "247"), class = "factor"), ChoiceSet = structure(c(1L, 1L, 
    1L, 1L, 1L, 1L), .Label = c("Baseline_Choice_1", "Baseline_Choice_2", 
    "Baseline_Choice_3", "Baseline_Choice_4", "SS_Green_1", "SS_Green_2", 
    "SS_Green_3", "SS_Green_4", "SS_Green_ESG_1", "SS_Green_ESG_2", 
    "SS_Green_ESG_3", "SS_Green_ESG_4", "SS_ESG_1", "SS_ESG_2", 
    "SS_ESG_3", "SS_ESG_4", "SS_Comp_Green_1", "SS_Comp_Green_2", 
    "SS_Comp_Green_3", "SS_Comp_Green_4", "SS_Comp_ESG_1", "SS_Comp_ESG_2", 
    "SS_Comp_ESG_3", "SS_Comp_ESG_4", "SS_Comp_1", "SS_Comp_2", 
    "SS_Comp_3", "SS_Comp_4", "SS_All_1", "SS_All_2", "SS_All_3", 
    "SS_All_4", "WTP_All_1", "WTP_All_2", "WTP_All_3", "WTP_All_4", 
    "WTP_Comp_1", "WTP_Comp_2", "WTP_Comp_3", "WTP_Comp_4", "WTP_Comp_ESG_1", 
    "WTP_Comp_ESG_2", "WTP_Comp_ESG_3", "WTP_Comp_ESG_4", "WTP_Comp_Green_1", 
    "WTP_Comp_Green_2", "WTP_Comp_Green_3", "WTP_Comp_Green_4", 
    "WTP_ESG_1", "WTP_ESG_2", "WTP_ESG_3", "WTP_ESG_4", "WTP_ESG_Green_1", 
    "WTP_ESG_Green_2", "WTP_ESG_Green_3", "WTP_ESG_Green_4", 
    "WTP_Green_1", "WTP_Green_2", "WTP_Green_3", "WTP_Green_4"
    ), class = "factor"), value = c("Off", "Off", "Off", "Off", 
    "Off", "Off"), Choice = c("Conventional", "Conventional", 
    "Conventional", "Conventional", "Conventional", "Conventional"
    ), price = c(1.5, 1.5, 1.5, 1.5, 1.5, 1.5)), row.names = c(NA, 
-6L), class = c("tbl_df", "tbl", "data.frame"))

score 0 · Answer 1 · answered Jun 12 '20 at 08:51

0

Is price not an attribute of the choices? The formula you have now models it as an attribute of the subjects, see the difference here from an example in the mlogit documentation:

## a pure "conditional" model
summary(mlogit(mode ~ price + catch, data = Fish)) #what you should have if price is an attribute of the choice options
## a pure "multinomial model"
summary(mlogit(mode ~ 0 | income, data = Fish)) #what you have now

So in your case reg.M <- mlogit::mlogit(formula = value ~ price, data = listDatasets[[2]])

What you did with multinom is what I mean (you fitted a conditional logit model, i.e., modeled price as an attribute of the choices). The model recognizes the levels of the dependent variable, but price in your model is modeled as a variable with a generic coefficient (one that is the same for all alternatives).

"...while working with multinomial logit models, one has to consider three kinds of variables : •

alternative specific variables xij with a generic coefficient β,
individual specific variables zi with an alternative specific coefficients γj ,
alternative specific variables wij with an alternative specific coefficient δj .

The satisfaction index for the alternative j is then : Vij = αj + βxij + γjzi + δjwij" (Source)

So if you want the third option from the list above, use this formula: reg.M <- mlogit::mlogit(formula = value ~ 0 | 1 | price, data = listDatasets[[2]])

answered Jun 12 '20 at 08:51

Ahorn

3,686
1
10
17

Thank you for your answer! Yes, price is an attribute of the choices and it does not change within a choice set. That means, Choice 1 = 1.5, Choice 2 = 1.5, Choice 3 = 1.5, Choice 4 = 1.3. I have 15 of these choice sets and the prices vary between but not within. Can I even use the `price` variable as a predictor? I tried the price as alternative specific variable, also tried your code aboce but I get the same mistake as before. – Mariella Jun 12 '20 at 10:13
I am thinking if I put all choice environments in one table (now one list is one choice-set) then it could work? Because every individual made 15 choices. The choices were always the same, but the price changed. – Mariella Jun 12 '20 at 10:17
Yes I think you should use all the choice situations at once and set the `panel` argument to `TRUE` – Ahorn Jun 12 '20 at 10:36
I transformed the table and have now everything as a panel but now it won't run any regression anymore. I tried to add `panel` and `rpar`. Do you know how I would have to specify the regression now? I include the `dput(head)` of my data above. – Mariella Jun 13 '20 at 09:39
`reg1 <- mlogit::mlogit(formula = Choice ~ price | ScoreEnvAtt, data = data_long, panel = TRUE, rpar= c(ScoreEnvAtt = "n", price = "n"))` I tried this for example – Mariella Jun 13 '20 at 09:39
Did you convert your data to the format `mlogit` wants first? With `mlogit.data` or `dfidx` in the newest package version. Please post a new question if it still doesn't work. Your question was about why you get the singularity error which I think I answered. Happy to provide more help but it is too cumbersome like this. – Ahorn Jun 13 '20 at 09:55

System is computationally singular using mlogit in R

1 Answers1