Specifying my model I ran into some very mild heteroscedasticity problems. Given its superior small-sample properties (my dataset contains 79 observations) I used the HC3 specification of the White heteroscedasticity robust standard errors. However it renders almost all my estimates non-significant. Playing around with the data it showed that the significance levels relied on the type of the robust standard error used (HC0 to HC3) to a large extent. Also I couldn't use HC3 on all my models, apparently because its performance relies on the size of the hat values.
Now I'm slightly confused. How can I decide between these different standard errors? I don't actually have many high leverage points so is HC3 even appropriate?
Some more information on the data: The sample size is fixed, as I'm working within comparative political science. My dependent variable is a left skewed 0-100 index. Most of the independent variables follow a normal distribution, those that don't were logged. Further a region-dummy is included
structure(list(ID = c("Afghanistan", "Albania", "Algeria", "Angola",
"Azerbaijan", "Bahrain", "Bangladesh", "Belarus", "Benin", "Bolivia",
"Burkina Faso", "Burma/Myanmar", "Burundi", "Cambodia", "Cameroon",
"Central African Republic", "Chad", "China", "Cuba", "Democratic Republic of the Congo",
"Djibouti", "Egypt", "Eritrea", "Eswatini", "Ethiopia", "Fiji",
"Gabon", "Guinea", "Haiti", "Honduras", "Hungary", "Iran", "Iraq",
"Jordan", "Kazakhstan", "Kenya", "Kuwait", "Kyrgyzstan", "Laos",
"Lebanon", "Madagascar", "Malawi", "Malaysia", "Mali", "Mauritania",
"Morocco", "Mozambique", "Nicaragua", "Niger", "Nigeria", "Oman",
"Pakistan", "Papua New Guinea", "Philippines", "Qatar", "Republic of the Congo",
"Russia", "Rwanda", "Saudi Arabia", "Serbia", "Singapore", "Somalia",
"South Sudan", "Sudan", "Syria", "Tajikistan", "Tanzania", "Thailand",
"Togo", "Turkey", "Turkmenistan", "Uganda", "Ukraine", "United Arab Emirates",
"Uzbekistan", "Venezuela", "Vietnam", "Zambia", "Zimbabwe"),
Dep_Var = c(84.26, 89.81, 92.13, 90.74, 96.3, 78.7, 93.52,
19.44, 70.83, 96.3, 89.81, 86.11, 33.33, 68.52, 71.3, 75.93,
88.89, 81.94, 100, 80.56, 100, 84.26, 93.52, 89.81, 80.56,
88.89, 81.48, 78.7, 87.04, 100, 76.85, 64.35, 96.3, 100,
89.35, 93.52, 100, 92.13, 96.3, 85.19, 95.37, 57.41, 75,
72.22, 77.78, 93.52, 80.56, 16.67, 61.11, 85.65, 100, 96.3,
83.8, 100, 86.11, 97.22, 87.04, 90.74, 94.44, 100, 85.19,
60.19, 86.11, 91.67, 86.11, 73.15, 50, 82.41, 73.15, 77.78,
58.33, 93.52, 92.59, 89.81, 96.3, 87.04, 96.3, 70.83, 87.96
), Var1 = c(4.127, 5.251, 5.296, 6.541, 6.672, 6.414, 6.78,
6.062, 7.056, 5.78, 5.786, 4.552, 3.537, 5.527, 5.608, 6.275,
3.147, 5.291, 6.55, 4.069, 4.996, 4.586, 4.605, 6.525, 5.409,
6.302, 6.324, 5.558, 3.996, 6.325, 5.951, 4.481, 3.772, 4.786,
6.746, 5.645, 6.613, 6.603, 6.306, 3.814, 5.482, 6.14, 6.521,
4.924, 5.121, 5.355, 5.101, 7.214, 6.554, 6.047, 5.636, 7.175,
4.735, 5.151, 6.116, 4.799, 5.495, 6.855, 6.197, 6.398, 7.468,
3.565, 3.891, 5.121, 3.319, 6.826, 5.235, 5.737, 5.703, 4.748,
5.693, 6.474, 5.836, 6.91, 5.616, 5.979, 5.604, 6.875, 6.48
), Var2 = c(7.71, 7.85, 6.22, 6.93, 5.95, 5.98, 7.46, 1.26,
3.65, 3.42, 5.84, 3.31, 8.72, 7.88, 6.46, 8.05, 8.86, 5.62,
4.89, 6.42, 7.13, 5.63, 7.67, 2.84, 4.66, 4.57, 5.63, 6.62,
8.63, 8.64, 5.01, 3.43, 8.81, 5.72, 6.67, 5.12, 7.09, 6.05,
3.51, 7.46, 6.88, 5.64, 4.48, 5.68, 7.64, 4.56, 5.4, 7.27,
3.74, 7.67, 5.2, 7.83, 8.17, 7.09, 8.66, 9.11, 4.12, 2.87,
6.84, 6.36, 1.83, 8.71, 7.95, 6.59, 7.53, 6.92, 3.77, 6.72,
5.77, 4.83, 8.15, 5.81, 4.23, 4.3, 5.46, 8.92, 1.94, 5.48,
7.55), Var3 = c(1.51522335168878, 4.15325778828397, 2.94875838540978,
1.00628430938346, 25.4230503312376, 8.18998374332489, 1.04538591988069,
1.25351605643943, 1.03389499888613, 1.14765788536537, 1.26573001102583,
1.07401182190831, 1.02601777187271, 1.03639332007889, 1.62605356699817,
1.92725573397033, 1.01254164138481, 1.03505721838858, 3.46173219653658,
1.08295832426121, 57.2882616377008, 1.20022298864129, NA,
1.43549075453128, 1.01873682901296, 1.44946193787762, 1.64439543970553,
1.00783008956213, 1.14205709505493, 1.08208397251952, 2.40225911107622,
22.5235306849493, 1.36123323295883, 1.14848994633969, 1.27546825552435,
1.15597071197187, 48.3011823156329, 1.24779693041552, 1,
2.15232361681418, 1.10011380715122, 1.05904852323133, 1.67293114440204,
1, 1.02209604887292, 1.26595913129412, 1.57959491321159,
1.04583300104408, 1.00857974540892, 1.16022802219023, 206.447814325508,
1.3232281172556, 1.01139457132996, 1.10081706683103, 3.18921374388388,
1.0557568170143, 1.23896346376779, 1.03959784429336, 17.1956183236117,
1.80633839574657, 10.3099601319805, 1.02590186237628, 1.02711959279389,
3.88462180786233, 1.03514910690513, 6.23547964396164, 1.00861987775186,
1.87180599797356, 1.19796183444303, 24.2411476428364, NA,
1.02032998088937, 1.91697325378271, 5.22699733044137, 2.96243967880312,
3.06551946990564, 1.07671406220387, 1.1343707501751, 1.01365610166913
), Var4 = c(5.02115486913067, 53.5285741103671, 39.4834327892571,
29.7359115979868, 47.9358701966989, 235.03977126673, 18.5573982408046,
66.6329529282582, 12.1943267185875, 35.520687621416, 7.748396902346,
14.0781314341043, 2.61247472515742, 16.4312138876475, 14.9790917560296,
4.67907440636335, 7.09540310138533, 102.616791283744, 88.2181889125004,
5.45216212311342, 34.0884625440838, 30.2003134971543, NA,
38.3702699384472, 8.57501351042922, 62.2004642089247, 76.6736686126914,
10.6413123736656, 7.5458791774842, 25.7491219067443, 164.757418389402,
55.2031078932382, 59.5510901036816, 43.3032934593257, 97.3114520688729,
18.165469164389, 320.319801025988, 13.0939299165512, 25.3489827724281,
77.8431685692976, 5.2221980923047, 4.11552340423602, 114.148376618668,
8.90737285506382, 16.7791925268633, 32.0409500313298, 4.91804723063735,
19.1290374537869, 5.54600968697425, 22.2985869624463, 154.740324753635,
12.8470204090039, 28.4518018574842, 34.8508421836621, 647.817331974169,
20.1107239887663, 115.849953826104, 8.01656186978807, 231.397986561214,
74.0235455862041, 652.332824392302, NA, NA, 4.41505603374484,
NA, 8.70787589323223, 11.2212181047515, 78.0819291629949,
6.75542213340634, 90.4249298288882, 69.6663541063077, 7.76768575885308,
36.5903131229487, 431.033230583165, 17.248411344137, NA,
27.1527603640721, 12.9134335737364, 14.6398591018054), Var5 = c(2.086,
5.23, 4.112, 2.896, 4.8, 5.36, 3.504, 4.398, 3.868, 4.356,
3.844, 2.862, 2.16, 3.862, 3.4, 1.56, 1.942, 5.954, 4.51,
1.89, 3.202, 3.83, 1.544, 3.68, 3.786, 5.52, 3.376, 3.058,
1.182, 3.758, 5.974, 4.14, 2.358, 5.226, 5.044, 4.178, 4.824,
3.776, 3.654, 3.72, 2.694, 3.542, 7.15, 2.99, 3.546, 4.582,
3.252, 3.396, 3.468, 2.954, 5.374, 3.732, 3.646, 5.1, 6.262,
2.566, 4.878, 5.414, 5.646, 5.224, 9.462, 0.618, 0.102, 1.76,
1.658, 2.804, 3.488, 5.7, 2.884, 5.012, 2.912, 3.788, 4.17,
7.862, 3.906, 1.836, 4.994, 3.882, 2.602), Var6 = c(43.2,
10.8, 7.5, 2.7, 21.5, 7.4, 27.4, 63.1, 1.5, 3.6, 1.1, 20,
1.4, 18.9, 27.7, 1.9, 0.8, 38.3, 32.4, 18.8, 3.2, 5.6, 1.6,
5, 42.2, 8.2, 14.5, 0.7, 1.6, 2.8, 41.4, 32, 5.6, 37.4, 42.8,
20.7, 39.9, 17.2, 21, 37.4, 0.6, 19, 26.6, 0.5, 1.1, 20.5,
18.1, 46.2, 17.1, 2.8, 26.9, 3.4, 22.7, 20.9, 52.6, 3.5,
47.3, 20.1, 56.3, 19.4, 56.6, 1.5, 27.1, 2.7, 7.8, 16.6,
1.4, 48.1, 1.3, 10.7, 22.2, 1.4, 28.2, 32.9, 22.7, 6.4, 24.1,
21, 3.9), Var7 = c(0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0,
0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
1, 0, 1, 0, 1, 0, 0, 0, 0), Var8 = c(0, 0, 0, 1, 0, 0, 0,
0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0,
1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1,
0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1,
0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1), Var9 = c(0,
0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0,
0, 0), Var10 = c(0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0), Var11 = c(0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
1, 0, 0, 0, 0, NA, 0, 0, 0, 0, 0, 0, 0, 0), Var12 = c(1L,
1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L,
1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L,
0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L,
0L, 1L, 1L)), row.names = c(1L, 2L, 3L, 5L, 11L, 12L, 13L,
15L, 18L, 21L, 28L, 29L, 30L, 31L, 32L, 36L, 37L, 39L, 43L, 46L,
48L, 52L, 54L, 56L, 57L, 59L, 62L, 71L, 73L, 74L, 76L, 80L, 81L,
88L, 89L, 90L, 92L, 93L, 94L, 96L, 103L, 104L, 105L, 106L, 107L,
113L, 114L, 119L, 120L, 121L, 123L, 124L, 127L, 130L, 135L, 136L,
138L, 139L, 141L, 143L, 146L, 150L, 153L, 156L, 160L, 162L, 163L,
164L, 167L, 170L, 171L, 173L, 174L, 175L, 179L, 181L, 182L, 184L,
185L), class = "data.frame")
model <- lm(formula = Dep_var ~ Var1 + Var2 + log(Var3) +
Var4 + Var5 + Var6 + Var7 + Var8 +
Var9 + Var10 + Var11 + Var12,
data = subset(df, ID !="Nicaragua" &
ID != "Belarus" &
ID != "Burundi"),
na.action = na.exclude)
coeftest(model, vcov = vcovHC(model, method = "arellano", type = "HC3"))
