Results

Linear Regression

This is a linear regression using additive log ratios, based on the method described by Coenders & Pawlowsky-Glahn (2020).

Model Fit Measures
Overall Model Test
ModelRAdjusted R²Fdf1df2p
10.9170.8410.7297.483448< .001

 

Model Coefficients - OutputsGPA
95% Confidence Interval
PredictorEstimateSELowerUppertp
Intercept2.953040.22652.497593.4084913.0365< .001
Log2(T1)_Log2(T3)0.046600.0322-0.018190.111381.44610.155
Log2(T2)_Log2(T3)-0.003850.0503-0.105020.09733-0.07650.939
Log2(T4)_Log2(T3)-0.008570.0196-0.048070.03094-0.43600.665
Log2(T5)_Log2(T3)-0.015350.0213-0.058180.02748-0.72070.475
Log2(T6)_Log2(T3)-0.004460.0171-0.038910.03000-0.26010.796
Log2(T7)_Log2(T3)0.010060.0178-0.025660.045780.56620.574
Log2(T8)_Log2(T3)0.034540.0210-0.007720.076801.64340.107
Log2(T9)_Log2(T3)-0.028840.0240-0.077000.01932-1.20420.234
Log2(T10)_Log2(T3)0.019350.0220-0.024900.063610.87930.384
Log2(T11)_Log2(T3)0.019690.0148-0.010080.049451.33000.190
Log2(T12)_Log2(T3)-0.018150.0154-0.049150.01284-1.17740.245
Log2(T13)_Log2(T3)-0.024220.0239-0.072350.02390-1.01190.317
Log2(T14)_Log2(T3)0.092480.0557-0.019580.204551.65940.104
Log2(T15)_Log2(T3)0.029490.0238-0.018410.077381.23780.222
Log2(T16)_Log2(T3)-0.049570.0274-0.104580.00544-1.81180.076
Log2(T17)_Log2(T3)-0.031250.0358-0.103250.04075-0.87260.387
Log2(T18)_Log2(T3)-0.003800.0315-0.067230.05962-0.12050.905
Log2(T19)_Log2(T3)-0.024090.0138-0.051770.00358-1.75020.086
Log2(T20)_Log2(T3)0.080790.03530.009730.151852.28600.027
Log2(T21)_Log2(T3)-0.007890.0171-0.042270.02649-0.46170.646
Log2(T22)_Log2(T3)0.104260.02770.048570.159963.7639< .001
Log2(T23)_Log2(T3)0.068280.0409-0.013950.150521.66960.102
Log2(T24)_Log2(T3)-0.020540.0292-0.079310.03823-0.70280.486
Log2(T25)_Log2(T3)-0.001940.0364-0.075210.07133-0.05320.958
Log2(T26)_Log2(T3)-0.017850.0467-0.111670.07597-0.38250.704
Log2(T27)_Log2(T3)-0.101720.0475-0.19723-0.00620-2.14120.037
Log2(T28)_Log2(T3)-0.014310.0304-0.075530.04691-0.47000.640
Log2(T29)_Log2(T3)0.002780.0187-0.034780.040340.14890.882
Log2(T30)_Log2(T3)-0.164370.0487-0.26228-0.06645-3.37520.001
Log2(T31)_Log2(T3)0.002820.0228-0.043020.048650.12350.902
Log2(T32)_Log2(T3)-0.076660.0872-0.251900.09858-0.87960.383
Log2(T33)_Log2(T3)-0.017840.0226-0.063310.02763-0.78870.434
Log2(T34)_Log2(T3)-0.003970.0262-0.056590.04865-0.15160.880
Log2(T35)_Log2(T3)0.024070.0164-0.008900.057041.46800.149

 

Assumption Checks

Collinearity Statistics
 VIFTolerance
Log2(T1)_Log2(T3)3.300.303
Log2(T2)_Log2(T3)7.800.128
Log2(T4)_Log2(T3)4.240.236
Log2(T5)_Log2(T3)4.060.247
Log2(T6)_Log2(T3)2.400.417
Log2(T7)_Log2(T3)3.160.316
Log2(T8)_Log2(T3)4.680.214
Log2(T9)_Log2(T3)2.630.381
Log2(T10)_Log2(T3)2.510.398
Log2(T11)_Log2(T3)2.340.427
Log2(T12)_Log2(T3)2.830.353
Log2(T13)_Log2(T3)1.690.593
Log2(T14)_Log2(T3)5.920.169
Log2(T15)_Log2(T3)5.110.196
Log2(T16)_Log2(T3)6.050.165
Log2(T17)_Log2(T3)2.320.430
Log2(T18)_Log2(T3)5.800.172
Log2(T19)_Log2(T3)3.190.313
Log2(T20)_Log2(T3)2.960.338
Log2(T21)_Log2(T3)2.210.453
Log2(T22)_Log2(T3)3.740.267
Log2(T23)_Log2(T3)4.690.213
Log2(T24)_Log2(T3)3.090.324
Log2(T25)_Log2(T3)5.440.184
Log2(T26)_Log2(T3)7.750.129
Log2(T27)_Log2(T3)3.210.312
Log2(T28)_Log2(T3)3.910.256
Log2(T29)_Log2(T3)2.850.351
Log2(T30)_Log2(T3)3.240.308
Log2(T31)_Log2(T3)2.490.401
Log2(T32)_Log2(T3)7.320.137
Log2(T33)_Log2(T3)3.450.290
Log2(T34)_Log2(T3)4.780.209
Log2(T35)_Log2(T3)2.670.374
[3]

 

Linear Regression

This is a linear regression using additive log ratios, based on the method described by Coenders & Pawlowsky-Glahn (2020). Dependent variable 4* %.

Model Fit Measures
Overall Model Test
ModelRAdjusted R²Fdf1df2p
10.9180.8420.7317.543448< .001

 

Model Coefficients - 4*
95% Confidence Interval
PredictorEstimateSELowerUppertp
Intercept34.30717.27919.67248.9434.7132< .001
Log2(T1)_Log2(T3)0.98001.035-1.1023.0620.94660.349
Log2(T2)_Log2(T3)-0.19581.617-3.4473.055-0.12110.904
Log2(T4)_Log2(T3)0.42270.631-0.8471.6920.66950.506
Log2(T5)_Log2(T3)0.77180.685-0.6052.1481.12750.265
Log2(T6)_Log2(T3)0.87120.551-0.2361.9781.58220.120
Log2(T7)_Log2(T3)0.16900.571-0.9791.3170.29600.768
Log2(T8)_Log2(T3)1.04960.675-0.3082.4081.55410.127
Log2(T9)_Log2(T3)-0.04490.770-1.5921.503-0.05840.954
Log2(T10)_Log2(T3)0.49020.707-0.9321.9120.69300.492
Log2(T11)_Log2(T3)-0.44050.476-1.3970.516-0.92610.359
Log2(T12)_Log2(T3)-0.22600.495-1.2220.770-0.45630.650
Log2(T13)_Log2(T3)-0.80520.769-2.3520.741-1.04700.300
Log2(T14)_Log2(T3)2.12501.791-1.4765.7261.18650.241
Log2(T15)_Log2(T3)1.10970.765-0.4292.6491.44960.154
Log2(T16)_Log2(T3)-1.43810.879-3.2060.330-1.63580.108
Log2(T17)_Log2(T3)-0.19701.151-2.5112.117-0.17120.865
Log2(T18)_Log2(T3)0.86171.014-1.1762.9000.85000.400
Log2(T19)_Log2(T3)-0.48260.442-1.3720.407-1.09110.281
Log2(T20)_Log2(T3)1.34061.136-0.9433.6241.18050.244
Log2(T21)_Log2(T3)-0.73610.549-1.8410.369-1.33960.187
Log2(T22)_Log2(T3)2.23700.8900.4474.0272.51310.015
Log2(T23)_Log2(T3)2.98031.3140.3385.6232.26770.028
Log2(T24)_Log2(T3)-1.07050.939-2.9590.818-1.13970.260
Log2(T25)_Log2(T3)-0.25021.171-2.6052.104-0.21370.832
Log2(T26)_Log2(T3)-1.28271.499-4.2971.732-0.85550.397
Log2(T27)_Log2(T3)-0.72021.526-3.7892.349-0.47180.639
Log2(T28)_Log2(T3)-0.29310.978-2.2601.674-0.29950.766
Log2(T29)_Log2(T3)-0.29660.600-1.5030.910-0.49420.623
Log2(T30)_Log2(T3)-7.47401.565-10.620-4.328-4.7761< .001
Log2(T31)_Log2(T3)-0.04710.733-1.5201.426-0.06430.949
Log2(T32)_Log2(T3)-4.51012.801-10.1411.121-1.61040.114
Log2(T33)_Log2(T3)-0.88240.727-2.3440.579-1.21430.231
Log2(T34)_Log2(T3)-0.13860.841-1.8291.552-0.16480.870
Log2(T35)_Log2(T3)0.41720.527-0.6421.4770.79190.432

 

Assumption Checks

Collinearity Statistics
 VIFTolerance
Log2(T1)_Log2(T3)3.300.303
Log2(T2)_Log2(T3)7.800.128
Log2(T4)_Log2(T3)4.240.236
Log2(T5)_Log2(T3)4.060.247
Log2(T6)_Log2(T3)2.400.417
Log2(T7)_Log2(T3)3.160.316
Log2(T8)_Log2(T3)4.680.214
Log2(T9)_Log2(T3)2.630.381
Log2(T10)_Log2(T3)2.510.398
Log2(T11)_Log2(T3)2.340.427
Log2(T12)_Log2(T3)2.830.353
Log2(T13)_Log2(T3)1.690.593
Log2(T14)_Log2(T3)5.920.169
Log2(T15)_Log2(T3)5.110.196
Log2(T16)_Log2(T3)6.050.165
Log2(T17)_Log2(T3)2.320.430
Log2(T18)_Log2(T3)5.800.172
Log2(T19)_Log2(T3)3.190.313
Log2(T20)_Log2(T3)2.960.338
Log2(T21)_Log2(T3)2.210.453
Log2(T22)_Log2(T3)3.740.267
Log2(T23)_Log2(T3)4.690.213
Log2(T24)_Log2(T3)3.090.324
Log2(T25)_Log2(T3)5.440.184
Log2(T26)_Log2(T3)7.750.129
Log2(T27)_Log2(T3)3.210.312
Log2(T28)_Log2(T3)3.910.256
Log2(T29)_Log2(T3)2.850.351
Log2(T30)_Log2(T3)3.240.308
Log2(T31)_Log2(T3)2.490.401
Log2(T32)_Log2(T3)7.320.137
Log2(T33)_Log2(T3)3.450.290
Log2(T34)_Log2(T3)4.780.209
Log2(T35)_Log2(T3)2.670.374
[3]

 

Correlation Matrix

This is a correlation matrix, looking at the relationships between each topic proportion, across units.

Correlation Matrix
  Avg_T32OutputsGPAAvg_T1Avg_T2Avg_T3Avg_T4Avg_T5Avg_T6Avg_T7Avg_T8Avg_T9Avg_T10Avg_T11Avg_T12Avg_T13Avg_T14Avg_T15Avg_T16Avg_T17Avg_T18Avg_T19Avg_T20Avg_T21Avg_T22Avg_T23Avg_T24Avg_T25Avg_T26Avg_T27Avg_T28Avg_T29Avg_T30Avg_T31Avg_T33Avg_T34Avg_T35
Avg_T32Pearson's r-0.585                                  
 df81                                  
 p-value< .001                                  
OutputsGPAPearson's r-0.585                                  
 df81                                  
 p-value< .001                                  
Avg_T1Pearson's r-0.1430.131                                 
 df8181                                 
 p-value0.1980.238                                 
Avg_T2Pearson's r-0.0730.0230.118                                
 df818181                                
 p-value0.5100.8390.290                                
Avg_T3Pearson's r-0.064-0.1750.034-0.434                               
 df81818181                               
 p-value0.5660.1130.764< .001                               
Avg_T4Pearson's r0.1910.059-0.093-0.003-0.235                              
 df8181818181                              
 p-value0.0840.5960.4050.9770.033                              
Avg_T5Pearson's r-0.2550.022-0.065-0.1360.025-0.142                             
 df818181818181                             
 p-value0.0200.8410.5580.2190.8250.202                             
Avg_T6Pearson's r0.094-0.128-0.134-0.2070.402-0.197-0.083                            
 df81818181818181                            
 p-value0.3980.2500.2280.060< .0010.0740.453                            
Avg_T7Pearson's r-0.3560.1840.111-0.1110.245-0.1870.541-0.025                           
 df8181818181818181                           
 p-value< .0010.0950.3180.3160.0260.091< .0010.824                           
Avg_T8Pearson's r0.2160.1520.0340.113-0.277-0.046-0.160-0.182-0.177                          
 df818181818181818181                          
 p-value0.0500.1720.7630.3090.0110.6790.1470.1000.110                          
Avg_T9Pearson's r-0.2280.284-0.039-0.068-0.1440.235-0.057-0.171-0.0060.009                         
 df81818181818181818181                         
 p-value0.0380.0090.7270.5400.1950.0320.6110.1230.9560.937                         
Avg_T10Pearson's r-0.3150.287-0.014-0.2310.161-0.0840.0650.0540.050-0.1250.020                        
 df8181818181818181818181                        
 p-value0.0040.0080.9020.0360.1460.4490.5610.6310.6510.2620.855                        
Avg_T11Pearson's r0.001-0.027-0.007-0.0230.1450.135-0.1170.040-0.072-0.0570.076-0.044                       
 df818181818181818181818181                       
 p-value0.9930.8080.9480.8340.1900.2230.2920.7180.5150.6110.4960.696                       
Avg_T12Pearson's r-0.3170.3120.335-0.1520.023-0.136-0.0410.058-0.019-0.021-0.0410.099-0.052                      
 df81818181818181818181818181                      
 p-value0.0040.0040.0020.1710.8340.2200.7100.6060.8620.8530.7140.3730.642                      
Avg_T13Pearson's r0.102-0.2890.070-0.1430.309-0.176-0.093-0.0390.0190.097-0.094-0.206-0.028-0.059                     
 df8181818181818181818181818181                     
 p-value0.3580.0080.5320.1960.0040.1110.4040.7230.8650.3840.3960.0620.8050.596                     
Avg_T14Pearson's r-0.0030.232-0.0770.183-0.4390.152-0.256-0.210-0.1990.1690.273-0.2340.035-0.153-0.129                    
 df818181818181818181818181818181                    
 p-value0.9770.0350.4900.098< .0010.1710.0200.0570.0720.1260.0130.0330.7530.1670.243                    
Avg_T15Pearson's r0.1290.1060.0610.388-0.4840.230-0.145-0.203-0.2140.161-0.093-0.137-0.001-0.055-0.2190.208                   
 df81818181818181818181818181818181                   
 p-value0.2450.3400.586< .001< .0010.0370.1900.0660.0520.1470.4010.2150.9920.6240.0470.059                   
Avg_T16Pearson's r0.103-0.0340.0030.026-0.2570.022-0.184-0.073-0.1980.061-0.013-0.0580.083-0.131-0.1540.0240.129                  
 df8181818181818181818181818181818181                  
 p-value0.3520.7580.9810.8160.0190.8430.0950.5100.0720.5860.9060.6040.4570.2370.1640.8300.244                  
Avg_T17Pearson's r0.283-0.391-0.143-0.1960.332-0.1230.0320.0890.020-0.078-0.022-0.198-0.047-0.1590.272-0.111-0.278-0.325                 
 df818181818181818181818181818181818181                 
 p-value0.010< .0010.1980.0760.0020.2670.7760.4210.8560.4810.8420.0730.6700.1500.0130.3180.0110.003                 
Avg_T18Pearson's r0.135-0.1270.2470.516-0.4140.013-0.144-0.160-0.1870.118-0.109-0.173-0.050-0.153-0.0630.1790.1930.235-0.118                
 df81818181818181818181818181818181818181                
 p-value0.2230.2530.024< .001< .0010.9070.1950.1500.0900.2870.3270.1170.6540.1660.5700.1040.0800.0330.288                
Avg_T19Pearson's r-0.2170.2300.013-0.036-0.089-0.012-0.039-0.053-0.062-0.057-0.0260.318-0.0140.158-0.157-0.0290.1750.157-0.252-0.143               
 df8181818181818181818181818181818181818181               
 p-value0.0480.0370.9040.7470.4210.9140.7280.6330.5770.6110.8140.0030.9030.1530.1570.7970.1140.1570.0220.198               
Avg_T20Pearson's r0.0920.059-0.131-0.127-0.0080.143-0.034-0.329-0.1240.0570.125-0.003-0.057-0.1530.0630.020-0.0780.0580.088-0.102-0.046              
 df818181818181818181818181818181818181818181              
 p-value0.4090.5970.2390.2540.9440.1970.7590.0020.2650.6080.2620.9760.6110.1670.5730.8610.4820.6020.4300.3580.677              
Avg_T21Pearson's r0.162-0.294-0.168-0.0850.037-0.039-0.0370.034-0.129-0.019-0.157-0.0550.156-0.126-0.048-0.192-0.1540.1180.0670.024-0.1040.178             
 df81818181818181818181818181818181818181818181             
 p-value0.1430.0070.1300.4430.7380.7280.7390.7580.2460.8680.1570.6210.1580.2570.6680.0810.1650.2890.5450.8300.3470.107             
Avg_T22Pearson's r-0.5890.593-0.029-0.2910.100-0.1370.0890.1090.153-0.1030.4100.444-0.0840.187-0.179-0.007-0.148-0.080-0.207-0.3290.255-0.070-0.136            
 df8181818181818181818181818181818181818181818181            
 p-value< .001< .0010.7920.0080.3690.2150.4260.3250.1670.354< .001< .0010.4480.0910.1060.9510.1830.4710.0610.0020.0200.5270.220            
Avg_T23Pearson's r-0.1890.423-0.056-0.196-0.0340.206-0.2130.0180.0380.0230.1640.105-0.0210.108-0.2970.0330.1000.144-0.093-0.2510.154-0.127-0.0570.346           
 df818181818181818181818181818181818181818181818181           
 p-value0.087< .0010.6140.0750.7630.0620.0540.8740.7300.8340.1380.3440.8540.3310.0060.7660.3700.1940.4020.0220.1640.2510.6110.001           
Avg_T24Pearson's r-0.0130.001-0.142-0.1210.377-0.0430.046-0.0160.138-0.211-0.0300.2270.234-0.0240.097-0.327-0.243-0.2590.065-0.212-0.0740.2650.079-0.052-0.212          
 df81818181818181818181818181818181818181818181818181          
 p-value0.9040.9900.1990.277< .0010.7000.6790.8860.2140.0550.7880.0390.0340.8320.3830.0030.0270.0180.5580.0540.5060.0150.4770.6430.054          
Avg_T25Pearson's r0.1810.036-0.186-0.089-0.2670.102-0.1580.186-0.2490.1370.073-0.027-0.065-0.065-0.2000.1980.1550.158-0.155-0.0250.066-0.1690.0200.2960.109-0.288         
 df8181818181818181818181818181818181818181818181818181         
 p-value0.1010.7490.0930.4260.0150.3570.1540.0930.0230.2180.5110.8100.5620.5570.0700.0730.1630.1550.1620.8250.5540.1280.8590.0070.3270.008         
Avg_T26Pearson's r0.0500.0580.0440.319-0.3710.260-0.259-0.187-0.1390.1530.164-0.4040.116-0.224-0.0890.5200.2170.1380.0130.250-0.0350.009-0.092-0.2380.080-0.3840.069        
 df818181818181818181818181818181818181818181818181818181        
 p-value0.6540.6030.6910.003< .0010.0180.0180.0900.2100.1680.139< .0010.2950.0410.422< .0010.0480.2140.9090.0230.7520.9390.4100.0300.470< .0010.534        
Avg_T27Pearson's r0.348-0.450-0.293-0.1850.222-0.1930.0720.069-0.146-0.013-0.077-0.116-0.110-0.2760.2460.055-0.200-0.3260.392-0.134-0.1390.146-0.086-0.188-0.4510.184-0.087-0.114       
 df81818181818181818181818181818181818181818181818181818181       
 p-value0.001< .0010.0070.0950.0430.0810.5150.5380.1890.9050.4910.2980.3240.0110.0250.6240.0700.003< .0010.2280.2090.1890.4420.090< .0010.0960.4320.305       
Avg_T28Pearson's r-0.1210.166-0.194-0.043-0.1770.012-0.141-0.059-0.085-0.0140.148-0.094-0.066-0.109-0.0490.4930.024-0.158-0.045-0.084-0.1010.018-0.1260.2310.000-0.1680.3830.2130.065      
 df8181818181818181818181818181818181818181818181818181818181      
 p-value0.2770.1330.0790.6960.1090.9120.2030.5950.4460.9010.1810.3970.5520.3270.659< .0010.8330.1530.6860.4500.3620.8730.2570.0360.9980.129< .0010.0540.561      
Avg_T29Pearson's r0.165-0.188-0.0490.007-0.037-0.063-0.086-0.010-0.168-0.030-0.023-0.0810.134-0.153-0.0520.0790.0840.439-0.109-0.0290.141-0.0100.053-0.183-0.071-0.0510.027-0.031-0.030-0.024     
 df818181818181818181818181818181818181818181818181818181818181     
 p-value0.1360.0890.6590.9480.7400.5690.4410.9260.1290.7900.8360.4680.2260.1680.6420.4800.452< .0010.3250.7950.2040.9300.6370.0980.5210.6450.8080.7780.7890.826     
Avg_T30Pearson's r0.405-0.6040.049-0.0190.1540.075-0.1920.044-0.123-0.158-0.208-0.251-0.025-0.2330.141-0.197-0.0890.0680.2660.030-0.2100.0780.319-0.468-0.003-0.141-0.1730.0560.042-0.1760.083    
 df81818181818181818181818181818181818181818181818181818181818181    
 p-value< .001< .0010.6600.8630.1660.4990.0810.6940.2670.1550.0590.0220.8250.0340.2040.0740.4230.5430.0150.7900.0560.4810.003< .0010.9800.2020.1170.6130.7060.1110.456    
Avg_T31Pearson's r-0.1490.2410.006-0.0720.153-0.0640.0200.0080.1840.0020.0150.030-0.1610.310-0.083-0.152-0.073-0.227-0.112-0.277-0.0890.109-0.0940.099-0.0540.257-0.152-0.2350.050-0.035-0.078-0.162   
 df8181818181818181818181818181818181818181818181818181818181818181   
 p-value0.1790.0280.9570.5170.1660.5680.8550.9460.0970.9880.8920.7850.1450.0040.4550.1700.5130.0390.3130.0110.4240.3250.4000.3740.6280.0190.1700.0320.6520.7550.4810.143   
Avg_T33Pearson's r-0.3940.348-0.003-0.2980.240-0.0780.0630.1010.191-0.050-0.0720.4350.0190.141-0.101-0.237-0.0920.107-0.235-0.2690.366-0.129-0.0260.4880.5370.0230.071-0.281-0.265-0.089-0.144-0.2530.006  
 df818181818181818181818181818181818181818181818181818181818181818181  
 p-value< .0010.0010.9810.0060.0290.4820.5700.3650.0830.6560.520< .0010.8640.2050.3640.0310.4090.3360.0330.014< .0010.2450.815< .001< .0010.8330.5220.0100.0160.4250.1940.0210.958  
Avg_T34Pearson's r-0.4350.210-0.012-0.1880.021-0.2010.591-0.0700.300-0.142-0.1100.261-0.0840.419-0.102-0.364-0.139-0.063-0.189-0.211-0.029-0.112-0.0700.179-0.0320.061-0.217-0.347-0.170-0.179-0.095-0.2620.2190.215 
 df81818181818181818181818181818181818181818181818181818181818181818181 
 p-value< .0010.0570.9120.0880.8470.068< .0010.5300.0060.2020.3210.0170.451< .0010.358< .0010.2090.5710.0870.0560.7920.3150.5320.1060.7730.5830.0490.0010.1240.1050.3940.0170.0460.051 
Avg_T35Pearson's r-0.3670.259-0.002-0.226-0.083-0.1390.068-0.089-0.027-0.106-0.1140.191-0.1490.513-0.102-0.090-0.1410.021-0.220-0.2090.101-0.006-0.1670.2340.1660.015-0.126-0.304-0.0280.024-0.106-0.2660.2130.1710.494
 df8181818181818181818181818181818181818181818181818181818181818181818181
 p-value< .0010.0180.9880.0400.4580.2090.5410.4220.8070.3400.3040.0830.177< .0010.3580.4180.2030.8490.0460.0570.3660.9560.1300.0330.1340.8910.2550.0050.8010.8290.3400.0150.0530.122< .001

 

References

[1] The jamovi project (2022). jamovi. (Version 2.3) [Computer Software]. Retrieved from https://www.jamovi.org.

[2] R Core Team (2021). R: A Language and environment for statistical computing. (Version 4.1) [Computer software]. Retrieved from https://cran.r-project.org. (R packages retrieved from MRAN snapshot 2022-01-01).

[3] Fox, J., & Weisberg, S. (2020). car: Companion to Applied Regression. [R package]. Retrieved from https://cran.r-project.org/package=car.