read data

df <- read.csv("lighting.csv")
str(df); head(df)
## 'data.frame':    1200 obs. of  5 variables:
##  $ observation   : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Country       : chr  "United States of America" "United States of America" "United States of America" "United States of America" ...
##  $ light         : chr  "light1" "light2" "light3" "light4" ...
##  $ Rater         : int  1 1 1 1 1 1 2 2 2 2 ...
##  $ average_rating: num  7 7.7 7.8 7.8 7.7 7.5 4.7 4.4 5 4.9 ...
##   observation                  Country  light Rater average_rating
## 1           1 United States of America light1     1            7.0
## 2           2 United States of America light2     1            7.7
## 3           3 United States of America light3     1            7.8
## 4           4 United States of America light4     1            7.8
## 5           5 United States of America light5     1            7.7
## 6           6 United States of America light6     1            7.5

Question one

“Can I run logistic regression with random factors. Please give me the R codes.”

Base Chat)

  • the answer provided is influenced by my conversation history – provides generic and specific examples And code with minimal explanation

ALISSTAIR)

Take a brief look at the key variables

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
country_avr <- df |> group_by(Country) |> summarize(avr_avr_country = mean(average_rating)) 
country_avr
## # A tibble: 2 × 2
##   Country                  avr_avr_country
##   <chr>                              <dbl>
## 1 India                               6.05
## 2 United States of America            5.08
rater_avr <- df |> group_by(Rater) |> summarize(avr_avr_rater = mean(average_rating)) 
rater_avr
## # A tibble: 200 × 2
##    Rater avr_avr_rater
##    <int>         <dbl>
##  1     1          7.58
##  2     2          4.82
##  3     3          2.6 
##  4     4          5.58
##  5     5          5.28
##  6     6          5.92
##  7     7          6.17
##  8     8          4.98
##  9     9          7.1 
## 10    10          5.83
## # ℹ 190 more rows

Light interpretation

unique(df$light)
## [1] "light1" "light2" "light3" "light4" "light5" "light6"
  1. 90° overhead box light,
  2. ring light,
  3. 45° superior box light,
  4. built-in camera flash,
  5. 2 straight on box lights, each 45° from midline, and
  6. natural light. Participants were instructed to maintain a neutral

Input interpretation into data

df <- 
  df |>
  mutate(light_labels = case_when(
    light == "light1" ~ "90° overhead box light",
    light == "light2" ~ "ring light",
    light == "light3" ~ "45° superior box light",
    light == "light4" ~ "built-in camera flash",
    light == "light5" ~ "2 straight-on 45° box lights",
    light == "light6" ~ "natural light"
  )) |> 
  select(light_labels, everything())

Detail :

- Volunteer survey respondents were instructed to rate the subject’s attractiveness on a scale of 0 to 10

Model 1)

Treating country and light as fixed factors, conduct multiple linear regression “lm”; using average rating as outcome with Country and light as fixed predictors.

m1<-lm(average_rating~Country+light, data=df)
summary(m1)
## 
## Call:
## lm(formula = average_rating ~ Country + light, data = df)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.5161 -0.6747  0.0086  0.6939  3.0333 
## 
## Coefficients:
##                                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      5.86668    0.09482  61.874  < 2e-16 ***
## CountryUnited States of America -0.96508    0.07226 -13.356  < 2e-16 ***
## lightlight2                      0.21450    0.11177   1.919  0.05520 .  
## lightlight3                      0.31050    0.11177   2.778  0.00555 ** 
## lightlight4                      0.20800    0.11177   1.861  0.06299 .  
## lightlight5                      0.20450    0.11177   1.830  0.06754 .  
## lightlight6                      0.15150    0.11177   1.356  0.17551    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.118 on 1193 degrees of freedom
## Multiple R-squared:  0.1354, Adjusted R-squared:  0.1311 
## F-statistic: 31.14 on 6 and 1193 DF,  p-value: < 2.2e-16

Details :

\[\textbf{Hypotheses (for coefficient $\beta_j$):}\] \[ H_0: \beta_j = 0 \] \[ H_a: \beta_j \neq 0 \]

\[\textbf{Test statistic:}\] \[ t = \frac{\hat{\beta}_j}{\text{SE}(\hat{\beta}_j)} \]

    -   Country is statistically significant

    -   Light 3 is Significant

-   $$
    F
    $$

The F-test in regression compares explained and unexplained variation: \[ F = \frac{\text{SSR}/p}{\text{SSE}/(n - p - 1)} \]

\[ \textbf{Hypotheses:} \] \[ H_0: \beta_1 = \beta_2 = \cdots = \beta_p = 0 \] \[ H_a: \text{at least one } \beta_j \neq 0 \]
A large \(F\) indicates that the explained variation is large relative to the residual variation, suggesting the model has explanatory power.

\[ R^2 \]

Interpretation :

png("boxplot_light.png", width = 800, height = 600)

boxplot(
  average_rating ~ light_labels,
  data = df,
  xaxt = "n"
)

labels <- levels(factor(df$light_labels))

text(
  seq_along(labels),
  par("usr")[3] - 0.2,
  labels = labels,
  srt = 45,
  adj = 1,
  xpd = TRUE,
  cex = 0.7
)

Interpretation :

  • Earlier we said these were sign.

    • lightlight2 0.21450 0.11177 1.919 0.05520 .

    • lightlight4 0.20800 0.11177 1.861 0.06299 .

    • lightlight5 0.20450 0.11177 1.830 0.06754 .

and,

df |> distinct(light_labels, light)
##                   light_labels  light
## 1       90° overhead box light light1
## 2                   ring light light2
## 3       45° superior box light light3
## 4        built-in camera flash light4
## 5 2 straight-on 45° box lights light5
## 6                natural light light6

so :

ring light light2
built-in camera flash light4
2 straight-on 45° box lights light5 
png("boxplot_country.png", width = 800, height = 600)
boxplot(df$average_rating~df$Country, horizontal = T)
  • As we can see country appears significant graphically

MSE)

\[ \text{MSE} = \frac{1}{n - p - 1} \sum_{i=1}^n (y_i - \hat{y}_i)^2 \\ = \frac{\text{SSE}}{n - p - 1} \]

  • Model error for every degree of freedom from our error

  • RMSE : square root of it : Average error

Calculation :

mse <- mean(residuals(m1)^2)
mse
## [1] 1.241887
sqrt(mse)
## [1] 1.1144
  • our model is typically off by about 1 rating point on average

Diagnostics:

plot(m1, which = 1)

plot(m1, which = 2)

  • error looks almost normally distributed – more like t but close

  • average error of 0 – really good

Interpretation :

  • Model assumptions dont seem 2 be violated
library(car)
library(effects)
## Warning: package 'effects' was built under R version 4.4.3
library(lattice)
plot(allEffects(m1),ask=FALSE)

  • These are the range of plausible values for the true mean rating under this lighting condition (holding other variables constant

\[ \textbf{Model:} \quad y_i = \beta_0 + \beta_{\text{light}_j} + \beta_{\text{Country}_k} + \varepsilon_i \]

\[ \textbf{Predicted mean (effect):} \quad \hat{\mu}_j = \mathbf{x}_j^\top \hat{\boldsymbol{\beta}} \]

\[ \textbf{Variance:} \quad \widehat{\mathrm{Var}}(\hat{\mu}_j) = \mathbf{x}_j^\top \widehat{\mathrm{Var}}(\hat{\boldsymbol{\beta}})\,\mathbf{x}_j \]

\[ \textbf{Standard Error:} \quad \mathrm{SE}(\hat{\mu}_j) = \sqrt{\mathbf{x}_j^\top \widehat{\mathrm{Var}}(\hat{\boldsymbol{\beta}})\,\mathbf{x}_j} \]

\[ \textbf{Interpretation:} \quad \text{CI}_j \approx \text{plausible values for } \mathbb{E}[Y \mid \text{light}=j, \text{others fixed}] \]

Where j is light level – we are seeing for each light level – using light1 as the baseline – we see what out model would predict given we are

Interpretation :

  • As we can see model choice vary dependent upon these variables – as stated earlier compared to our baseline holding others constant these lights look significant – notice 2, 4, 5 align
ring light light2
built-in camera flash light4
2 straight-on 45° box lights light5

Model 2)

library("lme4")

df$Country <- factor(df$Country)
df$light <- factor(df$light)
df$Rater <- factor(df$Rater)

m2 <- lmer(
  average_rating ~ Country + light + (1 | Rater),
  data = df
)

summary(m2)
## Linear mixed model fit by REML ['lmerMod']
## Formula: average_rating ~ Country + light + (1 | Rater)
##    Data: df
## 
## REML criterion at convergence: 1305.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.2105 -0.4611  0.0155  0.4517  3.8312 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Rater    (Intercept) 1.1735   1.0833  
##  Residual             0.0806   0.2839  
## Number of obs: 1200, groups:  Rater, 200
## 
## Fixed effects:
##                                 Estimate Std. Error t value
## (Intercept)                      5.86668    0.14804  39.629
## CountryUnited States of America -0.96508    0.17253  -5.594
## lightlight2                      0.21450    0.02839   7.555
## lightlight3                      0.31050    0.02839  10.937
## lightlight4                      0.20800    0.02839   7.326
## lightlight5                      0.20450    0.02839   7.203
## lightlight6                      0.15150    0.02839   5.336
## 
## Correlation of Fixed Effects:
##             (Intr) CnUSoA lghtl2 lghtl3 lghtl4 lghtl5
## CntryUntSoA -0.845                                   
## lightlight2 -0.096  0.000                            
## lightlight3 -0.096  0.000  0.500                     
## lightlight4 -0.096  0.000  0.500  0.500              
## lightlight5 -0.096  0.000  0.500  0.500  0.500       
## lightlight6 -0.096  0.000  0.500  0.500  0.500  0.500

Interpretation :

Fixed effects:
                                Estimate Std. Error t value
(Intercept)                      5.86668    0.14804  39.629
CountryUnited States of America -0.96508    0.17253  -5.594
lightlight2                      0.21450    0.02839   7.555
lightlight3                      0.31050    0.02839  10.937
lightlight4                      0.20800    0.02839   7.326
lightlight5                      0.20450    0.02839   7.203
lightlight6                      0.15150    0.02839   5.336

  • Our intercept is extremely significant – ie our Baseline rating (India + light1) is significant

  • Country is significant

  • US raters usually give about 1 pt lower than india – holding others constant

  • All lights increase rating

Random effects:
 Groups   Name        Variance Std.Dev.
 Rater    (Intercept) 1.1735   1.0833  
 Residual             0.0806   0.2839  
Number of obs: 1200, groups:  Rater, 200
  • Most variability is between raters, not noise

Which makes sense based on our previous graphic of the effects :

library(car)
library(effects)
library(lattice)
plot(allEffects(m1),ask=FALSE) 

vc <- as.data.frame(VarCorr(m2))

rater_var <- vc$vcov[vc$grp == "Rater"]
resid_var <- vc$vcov[vc$grp == "Residual"]

ICC <- rater_var / (rater_var + resid_var)
ICC
## [1] 0.9357286
  • as we can see about 94% pct of our variation in ratings is due to differences between raters.

Intercepts for each rater

ranef(m2)$Rater
##       (Intercept)
## 1    2.4719320423
## 2   -0.2634212244
## 3   -2.4549994442
## 4    0.4945682350
## 5   -0.7561918560
## 6    0.8241288696
## 7    1.0712993455
## 8   -0.0986409072
## 9    1.9940691222
## 10   0.7417387109
## 11  -2.9493403960
## 12   0.5110462667
## 13   0.9065190282
## 14   1.4832501387
## 15  -0.4776356369
## 16   1.2196016310
## 17   0.0002272832
## 18   1.3514258848
## 19  -1.2685811598
## 20  -0.6588939859
## 21  -0.5765038273
## 22  -0.0492068120
## 23   0.5604803619
## 24   0.0496613784
## 25  -0.7726698877
## 26   0.2473977591
## 27   1.5491622656
## 28  -0.4925433484
## 29   0.5110462667
## 30  -0.5765038273
## 31  -0.5435477638
## 32   0.2968318543
## 33   0.9065190282
## 34   0.1979636639
## 35   1.2211719513
## 36   0.3972703649
## 37   1.1372114724
## 38   0.2819241428
## 39  -0.5105917004
## 40   0.7433090312
## 41   0.2968318543
## 42   0.1155735053
## 43   0.4796605236
## 44  -0.0146804283
## 45  -0.5419774435
## 46   0.8900409965
## 47   1.8787229001
## 48   0.1995339842
## 49   0.5110462667
## 50   2.2592879501
## 51  -0.9884546204
## 52  -1.4498395088
## 53  -0.4266312214
## 54   1.5821183290
## 55  -1.2670108395
## 56  -1.0378887156
## 57  -0.6588939859
## 58   0.4616121716
## 59   0.3643143015
## 60  -1.6146198261
## 61  -1.9112243972
## 62  -0.3293333514
## 63  -2.4204730605
## 64   1.7468986463
## 65   1.2525576945
## 66  -1.6310978578
## 67  -1.0049326522
## 68  -0.2453728724
## 69  -1.5487076992
## 70  -0.2798992562
## 71  -0.6738016974
## 72  -1.0708447791
## 73   0.3133098860
## 74   1.7798547098
## 75  -0.0492068120
## 76  -1.4168834454
## 77  -2.2243070000
## 78   0.4961385553
## 79   0.3478362697
## 80   1.5821183290
## 81   0.2654461111
## 82   1.6496007762
## 83   0.4121780764
## 84   1.0218652503
## 85   0.4121780764
## 86  -2.1254388096
## 87   1.9462053473
## 88  -1.1038008425
## 89  -0.1315969706
## 90   0.8241288696
## 91   0.6758265840
## 92  -0.2798992562
## 93   1.5507325858
## 94   2.4554540106
## 95   0.0841877621
## 96  -1.2834888713
## 97   0.8406069013
## 98  -0.5254994118
## 99  -0.4611576052
## 100  1.7798547098
## 101  0.5275242985
## 102 -0.4446795734
## 103 -1.5487076992
## 104  1.3349478531
## 105  0.8406069013
## 106 -1.4977032837
## 107 -0.3458113831
## 108  0.3462659495
## 109  0.0167053149
## 110 -0.5105917004
## 111 -0.1810310658
## 112 -1.2356250964
## 113  2.6218046481
## 114  0.4451341398
## 115  0.7417387109
## 116  1.0383432820
## 117 -1.3674493502
## 118 -0.0821628754
## 119 -0.6902797291
## 120  0.4451341398
## 121 -0.7577621763
## 122 -0.6408456339
## 123  0.9740014754
## 124 -0.3787674465
## 125  1.1058257292
## 126  0.6758265840
## 127  1.6331227445
## 128 -1.0543667474
## 129  0.2803538226
## 130 -0.0162507485
## 131 -0.7742402080
## 132  1.3349478531
## 133  0.9080893485
## 134 -0.6588939859
## 135 -0.1810310658
## 136 -1.1846206809
## 137 -0.6588939859
## 138 -0.1975090975
## 139 -0.1810310658
## 140 -1.8453122703
## 141  0.2803538226
## 142 -0.2963772879
## 143 -0.1151189389
## 144  0.1155735053
## 145  0.7746947744
## 146  0.4451341398
## 147  0.3297879177
## 148 -0.6918500494
## 149 -0.3293333514
## 150  0.4121780764
## 151  2.3087220453
## 152  0.3462659495
## 153  0.6758265840
## 154 -0.4117235100
## 155  0.1485295687
## 156  0.4121780764
## 157 -0.3787674465
## 158 -0.3293333514
## 159 -0.6243676022
## 160  0.5126165870
## 161 -0.4117235100
## 162 -3.2789010306
## 163 -2.4863851874
## 164  0.1336218573
## 165  1.8128107732
## 166 -0.6408456339
## 167 -2.0430486510
## 168 -1.8288342385
## 169  0.0496613784
## 170  0.3148802063
## 171 -1.4812252520
## 172 -0.3936751580
## 173  0.1485295687
## 174 -0.9209721733
## 175 -0.5105917004
## 176  0.6428705206
## 177 -0.0162507485
## 178 -0.4117235100
## 179  0.2309197274
## 180 -0.7397138243
## 181  0.8570849330
## 182  0.0677097304
## 183 -0.2963772879
## 184 -0.5105917004
## 185  0.3148802063
## 186 -0.0986409072
## 187 -0.1315969706
## 188 -0.6078895705
## 189 -0.0970705869
## 190  0.0331833467
## 191 -0.1315969706
## 192  0.1336218573
## 193 -1.0378887156
## 194  2.0435032174
## 195  0.2984021746
## 196  0.1830559525
## 197  0.9229970599
## 198 -1.5651857309
## 199  0.9229970599
## 200 -2.3710389653

Diagnostics :

plot(m2)

  • Centered around 0, random variation clustered near 5

Model Comparison)

  • So it appears treating rater as a random effect our model is performing much better

Model 3)

m3 <- lmer(
  average_rating ~ Country + (1 | Rater) + (1 | light),
  data = df
)
summary(m3) 
## Linear mixed model fit by REML ['lmerMod']
## Formula: average_rating ~ Country + (1 | Rater) + (1 | light)
##    Data: df
## 
## REML criterion at convergence: 1299.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -5.2349 -0.4558  0.0162  0.4546  3.8356 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  Rater    (Intercept) 1.17349  1.0833  
##  light    (Intercept) 0.01016  0.1008  
##  Residual             0.08060  0.2839  
## Number of obs: 1200, groups:  Rater, 200; light, 6
## 
## Fixed effects:
##                                 Estimate Std. Error t value
## (Intercept)                       6.0482     0.1526  39.646
## CountryUnited States of America  -0.9651     0.1725  -5.594
## 
## Correlation of Fixed Effects:
##             (Intr)
## CntryUntSoA -0.820

Interpretation :

Random effects:
 Groups   Name        Variance Std.Dev.
 Rater    (Intercept) 1.17349  1.0833  
 light    (Intercept) 0.01016  0.1008  
 Residual             0.08060  0.2839  
Number of obs: 1200, groups:  Rater, 200; light, 6
  • Lighting doesnt really matter – notice its doing almost the same as our residuals – this is the main point of the experiment
Fixed effects:
                                Estimate Std. Error t value
(Intercept)                       6.0482     0.1526  39.646
CountryUnited States of America  -0.9651     0.1725  -5.594
  • However notice that country is still having a large effect

Intercepts for each rater

ranef(m3)$Rater
##       (Intercept)
## 1    2.4719320005
## 2   -0.2634212200
## 3   -2.4549994027
## 4    0.4945682267
## 5   -0.7561918432
## 6    0.8241288556
## 7    1.0712993274
## 8   -0.0986409055
## 9    1.9940690885
## 10   0.7417386984
## 11  -2.9493403462
## 12   0.5110462581
## 13   0.9065190129
## 14   1.4832501136
## 15  -0.4776356288
## 16   1.2196016104
## 17   0.0002272832
## 18   1.3514258620
## 19  -1.2685811384
## 20  -0.6588939748
## 21  -0.5765038175
## 22  -0.0492068112
## 23   0.5604803525
## 24   0.0496613775
## 25  -0.7726698747
## 26   0.2473977549
## 27   1.5491622394
## 28  -0.4925433400
## 29   0.5110462581
## 30  -0.5765038175
## 31  -0.5435477546
## 32   0.2968318493
## 33   0.9065190129
## 34   0.1979636606
## 35   1.2211719307
## 36   0.3972703582
## 37   1.1372114532
## 38   0.2819241381
## 39  -0.5105916917
## 40   0.7433090186
## 41   0.2968318493
## 42   0.1155735033
## 43   0.4796605155
## 44  -0.0146804280
## 45  -0.5419774344
## 46   0.8900409814
## 47   1.8787228684
## 48   0.1995339808
## 49   0.5110462581
## 50   2.2592879119
## 51  -0.9884546037
## 52  -1.4498394843
## 53  -0.4266312142
## 54   1.5821183023
## 55  -1.2670108181
## 56  -1.0378886981
## 57  -0.6588939748
## 58   0.4616121638
## 59   0.3643142953
## 60  -1.6146197988
## 61  -1.9112243649
## 62  -0.3293333458
## 63  -2.4204730195
## 64   1.7468986168
## 65   1.2525576733
## 66  -1.6310978302
## 67  -1.0049326352
## 68  -0.2453728683
## 69  -1.5487076730
## 70  -0.2798992514
## 71  -0.6738016860
## 72  -1.0708447610
## 73   0.3133098807
## 74   1.7798546797
## 75  -0.0492068112
## 76  -1.4168834214
## 77  -2.2243069624
## 78   0.4961385469
## 79   0.3478362639
## 80   1.5821183023
## 81   0.2654461066
## 82   1.6496007483
## 83   0.4121780694
## 84   1.0218652330
## 85   0.4121780694
## 86  -2.1254387737
## 87   1.9462053144
## 88  -1.1038008239
## 89  -0.1315969684
## 90   0.8241288556
## 91   0.6758265726
## 92  -0.2798992514
## 93   1.5507325596
## 94   2.4554539691
## 95   0.0841877607
## 96  -1.2834888496
## 97   0.8406068871
## 98  -0.5254994029
## 99  -0.4611575974
## 100  1.7798546797
## 101  0.5275242896
## 102 -0.4446795659
## 103 -1.5487076730
## 104  1.3349478305
## 105  0.8406068871
## 106 -1.4977032584
## 107 -0.3458113772
## 108  0.3462659436
## 109  0.0167053146
## 110 -0.5105916917
## 111 -0.1810310627
## 112 -1.2356250755
## 113  2.6218046038
## 114  0.4451341323
## 115  0.7417386984
## 116  1.0383432645
## 117 -1.3674493271
## 118 -0.0821628741
## 119 -0.6902797174
## 120  0.4451341323
## 121 -0.7577621635
## 122 -0.6408456231
## 123  0.9740014589
## 124 -0.3787674401
## 125  1.1058257105
## 126  0.6758265726
## 127  1.6331227169
## 128 -1.0543667295
## 129  0.2803538178
## 130 -0.0162507483
## 131 -0.7742401949
## 132  1.3349478305
## 133  0.9080893331
## 134 -0.6588939748
## 135 -0.1810310627
## 136 -1.1846206609
## 137 -0.6588939748
## 138 -0.1975090942
## 139 -0.1810310627
## 140 -1.8453122391
## 141  0.2803538178
## 142 -0.2963772829
## 143 -0.1151189370
## 144  0.1155735033
## 145  0.7746947613
## 146  0.4451341323
## 147  0.3297879122
## 148 -0.6918500377
## 149 -0.3293333458
## 150  0.4121780694
## 151  2.3087220063
## 152  0.3462659436
## 153  0.6758265726
## 154 -0.4117235030
## 155  0.1485295662
## 156  0.4121780694
## 157 -0.3787674401
## 158 -0.3293333458
## 159 -0.6243675916
## 160  0.5126165783
## 161 -0.4117235030
## 162 -3.2789009751
## 163 -2.4863851453
## 164  0.1336218550
## 165  1.8128107426
## 166 -0.6408456231
## 167 -2.0430486165
## 168 -1.8288342076
## 169  0.0496613775
## 170  0.3148802010
## 171 -1.4812252270
## 172 -0.3936751513
## 173  0.1485295662
## 174 -0.9209721577
## 175 -0.5105916917
## 176  0.6428705097
## 177 -0.0162507483
## 178 -0.4117235030
## 179  0.2309197235
## 180 -0.7397138118
## 181  0.8570849185
## 182  0.0677097292
## 183 -0.2963772829
## 184 -0.5105916917
## 185  0.3148802010
## 186 -0.0986409055
## 187 -0.1315969684
## 188 -0.6078895602
## 189 -0.0970705853
## 190  0.0331833461
## 191 -0.1315969684
## 192  0.1336218550
## 193 -1.0378886981
## 194  2.0435031829
## 195  0.2984021695
## 196  0.1830559494
## 197  0.9229970443
## 198 -1.5651857045
## 199  0.9229970443
## 200 -2.3710389252
ranef(m3)$light
##        (Intercept)
## light1 -0.17457368
## light2  0.03174067
## light3  0.12407716
## light4  0.02548872
## light5  0.02212229
## light6 -0.02885515

main conclusion :

  • Country and the person who’s rating matters most when rating attraction – makes sense.