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使用plm绘制固定效应模型中相互作用的预测值

[英]Plot predicted values for interaction in fixed effects model using `plm`

 原文  2013-05-15 20:22:57  9   1    r/ plm

问题描述

I'm struggling to graph the predicted probabilities generated by a repeated-measures experiment analyzed using the plm package. 我正在努力绘制使用plm软件包分析的重复测量实验所生成的预测概率图。

The experimental data I am analyzing is a repeated-measures experiment. 我正在分析的实验数据是重复测量实验。 People are asked to make 8 choices between different types of products. 人们被要求在不同类型的产品之间做出8种选择。 The order in which these products appear ( product , an 8-level factor variable) is randomized. 这些乘积出现的顺序（ product ，一个8级因子变量）是随机的。 At every point in time, a person is either assigned to a discount or no discount (the dichotomous var discount_i ). 在每个时间点，都会为一个人分配折扣或不给折扣（二分之一的var discount_i ）。

My theory posits that there is an interaction between a continous attitudinal variable ( iipm , 0-12) and the discount ( discount_i ), but not the product. 我的理论认为，连续的态度变量（ iipm ，0-12）和折扣（ discount_i ）之间存在相互作用，但产品之间没有相互作用。 Thus, my model is as follows: 因此，我的模型如下： 

fixed <- plm(chose ~ iipm*discount_i+factor(product), data=df, index=c("time", "id"), model="within", family='binomial')

I'm using a basic fixed effects model to account for time as well as dependence between observations, but I'm NOT INTERESTED in the effect of time, per say. 我正在使用一个基本的固定效应模型来考虑时间以及观察结果之间的依赖性，但是我对时间的影响并不感兴趣。 What I'd like to do is generate 8 product specific interaction plots of the predicted probability of choice, with the continuous variable ( iipm ) on the X-axis and the levels of discount_i being the two lines of predicted values . 我想要做的是产生的选择的预测概率的8产物的特异性相互作用图，其中的连续变量（ iipm在X轴）和水平discount_i是预测值的两行 。

Please help! 请帮忙！ A bit tricky for my current skill level. 我目前的技能水平有些棘手。

Sample data (which should be balanced, I hope!) below: 以下是示例数据（希望可以保持平衡！）： 

> dput(sample_data[1:128,])
structure(list(id = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 
1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 3L, 3L, 3L, 
3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 
5L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 
7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 
9L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 
11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 13L, 
13L, 13L, 13L, 13L, 13L, 13L, 13L, 14L, 14L, 14L, 14L, 14L, 14L, 
14L, 14L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L, 
16L, 16L, 16L, 16L, 16L), .Label = c(" A1FC4ZLFOKK2B9", " A22HZJIW9LEIS0", 
"A002160837SWJFPIAI7L7", "A09265903LS1OKAES4KAC", "A10B7OQ3GMIFD3", 
"A10ELK3KP57KWE", "A11F2KD14NFQ0A", "A11HTX95941MJI", "A12SMSQ6D5227J", 
"A12VWKFS6N0SV6", "A13HSR88OUNIVP ", "A14OFQMJ2Q6BTI", "A14OK6VJZDJ421 ", 
"A14W00II6N5ADC", "A14W0AXTJ3R19V", "A15DIISD5XBWHK", "A15E4I3BZKHNUV", 
"A1640357KEVPIW", "A1650FELH3UL2F", "A16KTSWXO8ZLMO", "A1835XBNR2UB4X", 
"A18ACKRAVMM8D8", "A18TXM6GMU1411", "A19F9CLZ0XWBYR", "A1A25FXEVMBSOA", 
"A1AJG4BGSRPC93", "A1AU8R78QWNKJD", "A1AYTEFEX5B89X", "A1BDBKDS7F7OMW", 
"A1BQEX75BE1AYE", "A1BXEU20OCUGVZ", "A1CAMCK95M88CN", "A1CIIX0CB0GR7H", 
"A1CTJ8UT7SF317", "A1ED68DLJ8YFWM", "A1EWHJ42DLEL37", "A1EWQ6YCM8CO0E", 
"A1F8MOWCCVDIH2", "A1GK40XYRMZHP7", "A1HFYKYYG9MW8G", "A1HI6CVPXJ70L1", 
"A1I2DD7WM94VC2", "A1I6551IZGYWM8", "A1ITBXITLY2952", "A1J4BNCH0HIQ98", 
"A1JMINVUZ2AOZR", "A1JMUSGZ7RN22X", "A1JXS7PBKBEVHT", "A1KEC6S4OBBE2U", 
"A1KJV3S1EK7LUT", "A1LMGLI5F2ZT4W", "A1M72TTFPE00AM", "A1NM7ZPZ3NH412", 
"A1OKNQ2JEXW34Q", "A1OQIXAU1SEJ4P", "A1OV86I0FAFAM1", "A1PA4WGAPB8LUV", 
"A1PLDF2A9RJD3J", "A1Q8L9UA8SAPIQ", "A1QK6O24KDVLJ1", "A1QR6I7UPY8XQJ", 
"A1QTQISKEHWSKZ", "A1R4F6EPXA3VCL", "A1R8A1ZKR80MRA", "A1S5W9N861BFLD", 
"A1SB15LP2XJVVT", "A1SG4CCCMLF8W2", "A1T5YMBH35PDBX ", "A1T78PV59MJ88L", 
"A1TH8X83SGT5ZE", "A1U81IXEMNUMX2", "A1UE8XA52IFAIV", "A1UH396UOK0X9Z", 
"A1WDSSOA9GW1T", "A1WUBD5BHESJVV", "A1XLGIFFGB01EU", "A1XSXTWJ4SDFXD", 
"A1YS3RYTSEXSGH", "A1YSYI926BBOHW", "A1ZERM9X4BHQV2", "A1ZHF9MHTINO5S", 
"A1ZN6M815BQV96", "A200LNG7PDSUGZ", "A209PPOU3RKN8E", "A20ASMCESA51U4", 
"A20IA63WXHF683", "A2177MS5XTPHK4", "A21ULKCLHVAACL", "A21YQXPL0SNNR2", 
"A220JLNQJ2WL33", "A22CF8BF9YQND7", "A22LZ62E0UC4VL", "A22R7DT2XQIKXV", 
"A22XK2FSFIAAFG", "A23AWSZSAGLY8X", "A23HJNY3F7Z9CS", "A23JA6ICO4BPQ5", 
"A243FYB6B3DG2S", "A244Q3FRPL4R3D", "A24LUXW1DB1QI5", "A257UIPAZR9NTN", 
"A25ZADCJI3D5AF", "A269JSFR6BWAW3", "A27CDEZVU8HL0N", "A27IABVBUZ9X8Z", 
"A27MJOV91GA8R3", "A28NJNZ3NRZ85T", "A28PG3NQXF9VAA", "A28QG7I54E4XAD", 
"A2958CGPRRIV04", "A29VL3MZE7YPBZ", "A2APPZDU0VS9LN", "A2AR2PLDAHHB28", 
"A2AU7FRKEQ0OHE", "A2AXGNA291U5BF", "A2BAFU5B5G2AVX", "A2BTJFHP7WQY23", 
"A2CWLWWRIK3IX3", "A2D2XQP00IZFR1", "A2DTTNGUXTEGHQ", "A2EEUQ0YY2XIU", 
"A2EHRNN23UBSJA", "A2EI075XZT9Y2S", "A2EM7RPFW3DU9N", "A2F2ASKIB0U2LM ", 
"A2FLCDTES3YD5I", "A2FZMW0KCCVLXR", "A2G8UI423QZYJJ", "A2GHZI45J9CN9R", 
"A2H18EYM79ZRCW", "A2H8GNSEVUJXYL", "A2HW7UTK78JAKG", "A2I7S2991CE4XO", 
"A2I9PUZT19ZBO8", "A2IRXCL5YW5RAS", "A2J6T9ELNZ97JH", "A2J7PEUIO2WVUN", 
"A2JVZUU107CL6Y", "A2KFOOEQWGN0GK", "A2NVUN3MHY8LMQ ", "A2OFN0A5CPLH57", 
"A2OW2CIT4H7364", "A2PPTAURU5AAQB", "A2QB3M030UWH53", "A2QLSHXNCHBRN4", 
"A2QZV6QX8WXJUN", "A2R10YXGQ9MTJ6", "A2R1CERP22ICFT", "A2R4B6OJPIW0HQ", 
"A2RMOCDLA2JSO5", "A2S96ZZ70YFPSK", "A2SPN23MCH9RKP", "A2TG7EEQ2XG2IK", 
"A2U81N228679L1", "A2UKT57LG0TWD1", "A2UO3QJZNC2VOE", "A2VDLRRPXV3N59", 
"A2VZB11NR1QC0S", "A2WLGVXAVT2XTR", "A2WZDY9R2GHRXD", "A2XM6C78S9L8UG", 
"A2XS49LRNX8PD4", "A2Y0SIZH81B265", "A2Y0ZGI29KQBTB", "A2YGVQGMU5AQYY", 
"A2YTOX7SEDJ1TC", "A2YYQJ3JWA2KGD", "A2Z8F0B2YGRFEY", "A30MS11FPNF1DS", 
"A316ZWBTQ7PGE7", "A31O3Y1D4EVLRP", "A321FJYVTX5WP9", "A321UTTHJSC5PO", 
"A32VLTWRJ1EP5T", "A32ZPYIWFEUCDX", "A33B6YFHZCMDUC", "A33BFK8KFKJ3IA", 
"A341G96EYJLBKF", "A347XXV5JH19PB", "A3485MZKNDDAMK", "A352QIC9QSCQEM", 
"A35OGKV242IJ78", "A3696JXTRKL2FI", "A372KQ73N0RZLJ", "A37533SGF100SL", 
"A37BWMULVPH2XJ", "A37I58C4258IPX", "A37NI374J4UNXD", "A37WXDYYT7RCZ0", 
"A3862RIFFUV141", "A38TCB4NTM5093", "A38USYKE9P7Z9O", "A39PGXN2A70UN5", 
"A39YE1VEL5T2XF", "A3ACR8IG31Q7K6", "A3AP1NCEBBR8S0", "A3APC5DH14Q0E2", 
"A3AWWFCNLAYW90", "A3B6BODCYK2O7L", "A3B6DOMIUDYB3I", "A3BFRHKQ94MZBX", 
"A3BM05OXSUCJII", "A3BUX2X4NAIB3K", "A3CCBRS9NU71R8", "A3CO5374TFUFEK", 
"A3D7JEGMSYKCUJ", "A3DD0FNVTIY7GO", "A3DU2ZHN459R53", "A3E8SXH0BAYG85", 
"A3EU5A0CGLUBRZ", "A3FDSQADGUY42E", "A3FG68U6LZ8EGN", "A3FWFXTCHEX9UM", 
"A3G9MSZVWB7W42", "A3GPR8TTDAX01S", "A3HKOZ90IDUZ8Z", "A3HLCR4YCHJWBI", 
"A3HQYWUW66HG1J", "A3IE6ATDKX6N1H", "A3J22SWYT5NPX6", "A3JZS32RQUWGJM", 
"A3KWA2ORU9M9IF", "A3M5CBY1V1FCX2", "A3MWV912LNFD67", "A3NH3BCC6GHEWR", 
"A3O1L0034OG341", "A3OWP3M7I9AQ44", "A3Q45OPFL3R49", "A3Q4T34SDWIHU9", 
"A3QB0Z9AN62HFH", "A3QM71HR4ZP65N", "A3QSJY1FFN0N6V", "A3QY3I5O0STFGA", 
"A3RTMAO8QC1Z97", "A3T7N659X3PGKV", "A3TBA7X9EF16W6", "A3TFAAGSW70079", 
"A3TXO6RKFIDFUV", "A3UX6ETXQOCG65", "A3VIM82WAK5TIZ", "A3W1LG4JXLNCL", 
"A50BRZM8LHWCD", "A5N8JGDID098C", "A669K8QT6PVVF", "A6IVYRP8FAIS", 
"A7D1FSJZSM3MJ", "A7EUXC5Q4675O", "A7I3G380E29VE", "A8BFVGGZ06DEC", 
"A8BLFGJE6RDQK", "A8FAG8ZFEM7FP", "A9JLQEN9J5WL3", "A9KJJHT79BXS8", 
"AA7ZQGZUR6V5E", "AAVJV2EYBWESX", "AC5LU9TF9CTK9", "ACJJUQ96T22RC", 
"ACNM6EM54CKRT", "ACPHZ1AG8XAQ0", "ACWYF9Z50PCA9", "ACZXP89TIXCUA", 
"ADQKQCMH1ALS6", "AEQWOTF1QN1MK", "AFB9N61OMZXCX", "AFHAH1BIN51GI ", 
"AG4LR5A7TCRH9", "AG7WQ3TB100SO", "AGF9EJ5F4E45D", "AGJ6958FU8A4N", 
"AHMFDP04U8I02", "AI1JF1C8UK1CX", "AIC8ALJV5X9OY", "AJB0OAEIYGY87", 
"AJETFLAXRDTKJ", "AJSTOFYJCC87B", "AM2V91APQ1DYH", "ANUXUJE8QRE0C", 
"AO3XB5I5QNNUI", "AO4ZHD0B9KUNE", "AOF7TQQOL7IT8", "AOKQZBHA40IBW", 
"AOLU7V2SEBS75", "AOT04CJ43L5V1", "AOVB3KCIIJLRJ", "APC3O2O8O9XPO", 
"APGX2WZ59OWDN", "AQ36OBO2GRA00", "AQ7YZUJW31SEL", "AQEVAKQLI09EN", 
"AQLG9XLOAUWUH", "AR95C0P53AFWJ", "ARVSVYBL46LC9", "AS3BSFKKBAN8J", 
"AS8XVJ2TNN58J", "ASH55LLJVVBOZ", "ASXIEBMMWW1NE", "AT0COJ1G23ZB0", 
"AT3HYOVRFTGNH", "ATHS9GUME1XCA", "ATJQG32KDCYMO", "AULC5HR1BBHMA", 
"AUN8AE8UCO3MD", "AUO7XEZDY9496", "AUSCGO1H49UY2", "AV5PNRD316L5R", 
"AVZ76FUE8VET9", "AWPAWDDLEEPTC", "AYG3MF094634L", "AYQWBIUVDPBXK", 
"AYSX5GNO640MZ", "AYZ85PU887QY1", "AZ1RJVNOZFIWV", "AZA8EVH0RZAR9", 
"AZCV8JQ2NEFN8", "AZOAW8JH5HJJK"), class = "factor"), product = c("Soap", 
"Chocolate", "Shampoo", "Batteries", "Tees", "Cleaner", "Jelly", 
"Coffee", "Soap", "Chocolate", "Shampoo", "Batteries", "Tees", 
"Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", 
"Batteries", "Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", 
"Shampoo", "Batteries", "Tees", "Cleaner", "Jelly", "Coffee", 
"Soap", "Chocolate", "Shampoo", "Batteries", "Tees", "Cleaner", 
"Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", "Batteries", 
"Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", 
"Batteries", "Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", 
"Shampoo", "Batteries", "Tees", "Cleaner", "Jelly", "Coffee", 
"Soap", "Chocolate", "Shampoo", "Batteries", "Tees", "Cleaner", 
"Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", "Batteries", 
"Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", 
"Batteries", "Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", 
"Shampoo", "Batteries", "Tees", "Cleaner", "Jelly", "Coffee", 
"Soap", "Chocolate", "Shampoo", "Batteries", "Tees", "Cleaner", 
"Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", "Batteries", 
"Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", "Shampoo", 
"Batteries", "Tees", "Cleaner", "Jelly", "Coffee", "Soap", "Chocolate", 
"Shampoo", "Batteries", "Tees", "Cleaner", "Jelly", "Coffee"), 
    chose = c(1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 
    0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 
    1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 
    1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 
    1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 
    1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
    1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1), discount_i = c(1, 
    1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 
    1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 
    0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 
    0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 
    0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 
    1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 
    1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0), iipm = c(9, 4, 9, 
    4, 4, 9, 4, 4, 12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 
    0, 0, 0, 0, 10, 10, 10, 8, 10, 10, 6, 8, 4, 3, 4, 1, 3, 4, 
    0, 1, 8, 4, 8, 8, 4, 8, 3, 8, 7, 6, 7, 0, 6, 7, 4, 0, 9, 
    11, 9, 4, 11, 9, 2, 4, 8, 7, 8, 4, 7, 8, 4, 4, 4, 10, 4, 
    0, 10, 4, 7, 0, 6, 8, 6, 8, 8, 6, 2, 8, 7, 7, 7, 4, 7, 7, 
    5, 4, 1, 8, 1, 5, 8, 1, 5, 5, 11, 9, 11, 10, 9, 11, 7, 10, 
    11, 10, 11, 11, 10, 11, 9, 11, 5, 8, 5, 4, 8, 5, 7, 4), time = c(7, 
    1, 8, 4, 2, 6, 5, 3, 7, 8, 5, 3, 4, 2, 1, 6, 4, 3, 1, 2, 
    6, 8, 7, 5, 1, 4, 7, 6, 8, 3, 5, 2, 3, 6, 1, 5, 4, 8, 7, 
    2, 3, 8, 2, 6, 4, 7, 1, 5, 2, 1, 8, 7, 3, 5, 4, 6, 4, 2, 
    3, 7, 1, 8, 6, 5, 5, 2, 6, 7, 3, 4, 8, 1, 7, 1, 8, 5, 3, 
    6, 4, 2, 1, 5, 3, 4, 7, 2, 6, 8, 6, 3, 4, 2, 1, 5, 8, 7, 
    6, 4, 2, 3, 8, 5, 7, 1, 7, 1, 8, 3, 2, 5, 4, 6, 1, 6, 3, 
    7, 8, 2, 4, 5, 3, 8, 5, 6, 1, 7, 4, 2)), .Names = c("Q97", 
"product", "chose", "discount_i", "iipm", "time"), row.names = c("108.soap", 
"108.choc", "108.shampoo", "108.batt", "108.tee", "108.clean", 
"108.jelly", "108.coffee", "220.soap", "220.choc", "220.shampoo", 
"220.batt", "220.tee", "220.clean", "220.jelly", "220.coffee", 
"241.soap", "241.choc", "241.shampoo", "241.batt", "241.tee", 
"241.clean", "241.jelly", "241.coffee", "152.soap", "152.choc", 
"152.shampoo", "152.batt", "152.tee", "152.clean", "152.jelly", 
"152.coffee", "247.soap", "247.choc", "247.shampoo", "247.batt", 
"247.tee", "247.clean", "247.jelly", "247.coffee", "205.soap", 
"205.choc", "205.shampoo", "205.batt", "205.tee", "205.clean", 
"205.jelly", "205.coffee", "173.soap", "173.choc", "173.shampoo", 
"173.batt", "173.tee", "173.clean", "173.jelly", "173.coffee", 
"132.soap", "132.choc", "132.shampoo", "132.batt", "132.tee", 
"132.clean", "132.jelly", "132.coffee", "78.soap", "78.choc", 
"78.shampoo", "78.batt", "78.tee", "78.clean", "78.jelly", "78.coffee", 
"10.soap", "10.choc", "10.shampoo", "10.batt", "10.tee", "10.clean", 
"10.jelly", "10.coffee", "137.soap", "137.choc", "137.shampoo", 
"137.batt", "137.tee", "137.clean", "137.jelly", "137.coffee", 
"114.soap", "114.choc", "114.shampoo", "114.batt", "114.tee", 
"114.clean", "114.jelly", "114.coffee", "304.soap", "304.choc", 
"304.shampoo", "304.batt", "304.tee", "304.clean", "304.jelly", 
"304.coffee", "149.soap", "149.choc", "149.shampoo", "149.batt", 
"149.tee", "149.clean", "149.jelly", "149.coffee", "21.soap", 
"21.choc", "21.shampoo", "21.batt", "21.tee", "21.clean", "21.jelly", 
"21.coffee", "107.soap", "107.choc", "107.shampoo", "107.batt", 
"107.tee", "107.clean", "107.jelly", "107.coffee"), class = "data.frame")

1 个解决方案

解决方案1
 0  2013-05-15 21:56:40

This may be close to what you want. 这可能接近您想要的。 

interaction.plot(df$iipm, df$product, predict(fixed), col = 2:9, lty = 1)

在此处输入图片说明

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相关问题 用R绘制预测值并比较随机效应plm模型中的相互作用项的最佳方法是什么？ - What is the best way in R to plot predicted values and compare interaction terms in a random effects plm model? plm：使用 fixef() 手动计算固定效应双向模型的拟合值 - plm: using fixef() to manually calculate fitted values for a fixed effects twoways model model 在 R 中的 plm package 中具有三个固定效果 - model with three fixed effects in plm package in R 包括 plm 中固定效应 model 中的非线性 - including non linearity in fixed effects model in plm 在 ggplot 中绘制具有固定效应交互作用的混合效应模型 - plot mixed effect model with interaction in fixed effects in ggplot 从固定效应模型 (plm) 绘制交互项 - Plotting interaction terms from fixed effects models (plm) 使用R中的plm fom model.matrix估计固定效应模型 - Estimate fixed effects model using plm fom model.matrix in R 使用 plm 固定效果回归 - Fixed effects regression with plm PLM 的边际效应 plot - Marginal effects plot of PLM plm 固定效应错误 - R 中的空模型 - 不平衡数据 - plm fixed effects error - empty model in R - unbalanced data
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