Interpreting mixed effects model results. Why are my coefficients for mixed effects model are so large?

Question

I am an economics grad student and I am in the process of writing a paper disproving using the Gini coefficient as a solitary measure of income inequality in migration determinants analysis.

I have taken Gini and migration rates from different countries for two time periods and ran a mixed model where random effects was Gini and AbroadIncome, and fixed effect was whether the country was 'Rich_Poor_Indicator'.

The idea was that Gini coefficient is not a sufficient measure of income inequality as a determinant for migration (I have done lit. review prior), so I expected some garbage results, but I feel like my model is too bizarre.

Here is the output with the formula:

Linear mixed model fit by REML ['lmerMod']
Formula: Migration ~ Rich_Poor_Indicator + (1 + Gini | Country.Name) +  
   AbroadIncome + (AbroadIncome | Country.Name)
  Data: final_data
Control: lmerControl(check.nobs.vs.nRE = "ignore")

REML criterion at convergence: 4655.9

Scaled residuals: 
   Min      1Q  Median      3Q     Max 
-5.7835 -0.1890 -0.0457  0.1119  6.5108 

Random effects:
Groups         Name         Variance  Std.Dev.  Corr 
Country.Name   (Intercept)  3.033e+11 550753.08      
               Gini         3.810e+09  61729.20 -0.42
Country.Name.1 (Intercept)  2.471e+11 497112.89      
               AbroadIncome 1.364e+03     36.93 1.00 
Residual                    1.780e+11 421957.35      
Number of obs: 153, groups:  Country.Name, 89

Fixed effects:
                        Estimate Std. Error t value
(Intercept)             1.203e+06  3.084e+05   3.901
Rich_Poor_IndicatorMid  2.070e+05  2.922e+05   0.708
Rich_Poor_IndicatorHigh 1.884e+05  3.599e+05   0.524
AbroadIncome            4.978e+00  5.961e+01   0.084

Correlation of Fixed Effects:
           (Intr) R_P_IM R_P_IH
Rch_Pr_IndM -0.546              
Rch_Pr_IndH -0.652  0.635       
AbroadIncom  0.037  0.004  0.077
fit warnings:
Some predictor variables are on very different scales: consider rescaling
optimizer (nloptwrap) convergence code: 0 (OK)
boundary (singular) fit: see ?isSingular

But, my CIs and Random Effects per each country are more comprehensible! But Gini does not show up in Random Effects...

CIs

Computing bootstrap confidence intervals ...

383 message(s): boundary (singular) fit: see ?isSingular
252 warning(s): Model failed to converge with max|grad| = 0.264562 (tol = 0.002, component 1) (and others)

                               2.5 %       97.5 %
.sig01                   1.256697e+01 2.401887e+06
.sig02                  -9.928984e-01 6.604565e-01
.sig03                   4.208632e+04 9.651804e+04
.sig04                   7.887378e+01 1.627314e+06
.sig05                  -1.000000e+00 1.000000e+00
.sig06                   1.215940e+00 4.086320e+02
.sigma                   3.244136e+05 4.811134e+05
(Intercept)              6.679768e+05 1.873740e+06
Rich_Poor_IndicatorMid  -3.883818e+05 7.826973e+05
Rich_Poor_IndicatorHigh -5.643505e+05 7.930619e+05
AbroadIncome            -1.591774e+02 1.744238e+02 

Random Effects

ranef(mix_model)$Country.Name
                    (Intercept)        Gini (Intercept) AbroadIncome
Algeria              -7446.2412   4451.2294    8980.157    0.6670574
Argentina            43191.8751 -18340.8448  -25998.904   -1.9312313
Armenia              38682.2221 -18581.0017  -29973.432   -2.2264643
Australia            39926.3675 -29014.5905  -65750.935   -4.8840623
Austria              34477.4962 -26956.5430  -65238.233   -4.8459781
Bangladesh         -125521.7158 111794.9842  291254.949   21.6347845
Belarus             -95005.4210  26977.6087    6192.779    0.4600074
Belgium              34126.4423 -33087.1346  -94934.288   -7.0518385
Belize               60286.3676 -23623.0023  -27433.462   -2.0377921
Benin                39787.0007 -21281.5020  -39571.309   -2.9394067
Bolivia              46788.4767 -18622.8722  -22439.365   -1.6668243
Botswana             58262.5126 -22310.0691  -24148.621   -1.7937900
Brazil               51117.2733 -13322.0661    2669.639    0.1983042
Bulgaria             27963.1360 -17092.4417  -35819.130   -2.6606901
Burkina Faso         55388.0338  -2956.0938   43594.547    3.2382579
Burundi              31971.0802 -26061.9075  -65023.664   -4.8300397
Cameroon             50944.1843 -24683.1290  -40962.994   -3.0427828
Canada                 887.1362  -5137.1674  -15053.915   -1.1182238
Chad                 50077.7077 -25918.0053  -45854.910   -3.4061605 

Sorry for the messy formatting, I am still learning how to use this platform! Any help is appreciated! Thanks in advance!

Answer 1

Ok there are a few problems here.

1. You have random slopes for gini but you do not specify it as a fixed effect. It's your main exposure so it should be a fixed effect.

2. The model has a singular fit. By removing gini as a random slope this may fix that although it's likely that AbroadIncome is causing that.

I would suggest starting with the following model:

Migration ~ Rich_Poor_Indicator +  Gini + AbroadIncome + (1 | Country.Name)

If this is supported by the data then you can consider adding random slopes.

Answer 2

One potential reason for the large CIs could be that the mixed effect model you are using is inappropriate for this analysis or miss-specified. Could you please show how your model is constructed (i.e. present the model formula)? I am unsure why you are using the Gini and AbroadIncome coefficients as random effects? To the extent of my knowledge, random effects for mixed effect models should be categorical and not continuous.

From the information you supplied above, I am unsure whether a mixed-effect model is even suitable for this kind of analysis. The coefficient tables you posted suggest that the rich_poor_Indicator only has two categories. For mixed effect models, it is generally suggested to have 5 or more categories within a response variable (This tutorial may be helpful as it offers an explanation of random and fixed effects). You may thus be better of using an interaction term between Gini and AbroadIncome with rich_poor_Indicator.

Sorry if this does not directly answer your question but I hope it helps!