Panel Data Estimators — plm • plm

Linear models for panel data estimated using the lm function on transformed data.

plm(
  formula,
  data,
  subset,
  weights,
  na.action,
  effect = c("individual", "time", "twoways", "nested"),
  model = c("within", "random", "ht", "between", "pooling", "fd"),
  random.method = NULL,
  random.models = NULL,
  random.dfcor = NULL,
  inst.method = c("bvk", "baltagi", "am", "bms"),
  restrict.matrix = NULL,
  restrict.rhs = NULL,
  index = NULL,
  ...
)

# S3 method for class 'plm.list'
print(
  x,
  digits = max(3, getOption("digits") - 2),
  width = getOption("width"),
  ...
)

# S3 method for class 'panelmodel'
terms(x, ...)

# S3 method for class 'panelmodel'
vcov(object, ...)

# S3 method for class 'panelmodel'
fitted(object, ...)

# S3 method for class 'panelmodel'
residuals(object, ...)

# S3 method for class 'panelmodel'
df.residual(object, ...)

# S3 method for class 'panelmodel'
coef(object, ...)

# S3 method for class 'panelmodel'
print(
  x,
  digits = max(3, getOption("digits") - 2),
  width = getOption("width"),
  ...
)

# S3 method for class 'panelmodel'
update(object, formula., ..., evaluate = TRUE)

# S3 method for class 'panelmodel'
deviance(object, model = NULL, ...)

# S3 method for class 'plm'
formula(x, ...)

# S3 method for class 'plm'
plot(
  x,
  dx = 0.2,
  N = NULL,
  seed = 1,
  within = TRUE,
  pooling = TRUE,
  between = FALSE,
  random = FALSE,
  ...
)

# S3 method for class 'plm'
residuals(object, model = NULL, effect = NULL, ...)

# S3 method for class 'plm'
fitted(object, model = NULL, effect = NULL, ...)

Arguments

formula: a symbolic description for the model to be estimated,
data: a data.frame,
subset: see stats::lm(),
weights: see stats::lm(),
na.action: see stats::lm(); currently, not fully supported,
effect: the effects introduced in the model, one of "individual", "time", "twoways", or "nested",
model: one of "pooling", "within", "between", "random" "fd", or "ht",
random.method: method of estimation for the variance components in the random effects model, one of "swar" (default), "amemiya", "walhus", "nerlove"; for Hausman-Taylor estimation set to "ht" (see Details and Examples),
random.models: an alternative to the previous argument, the models used to compute the variance components estimations are indicated,
random.dfcor: a numeric vector of length 2 indicating which degree of freedom should be used,
inst.method: the instrumental variable transformation: one of "bvk", "baltagi", "am", or "bms" (see also Details),
restrict.matrix: a matrix which defines linear restrictions on the coefficients,
restrict.rhs: the right hand side vector of the linear restrictions on the coefficients,
index: the indexes,
...: further arguments.
x, object: an object of class "plm",
digits: number of digits for printed output,
width: the maximum length of the lines in the printed output,
formula.: a new formula for the update method,
evaluate: a boolean for the update method, if TRUE the updated model is returned, if FALSE the call is returned,
dx: the half–length of the individual lines for the plot method (relative to x range),
N: the number of individual to plot,
seed: the seed which will lead to individual selection,
within: if TRUE, the within model is plotted,
pooling: if TRUE, the pooling model is plotted,
between: if TRUE, the between model is plotted,
random: if TRUE, the random effect model is plotted,

Value

An object of class "plm".

A "plm" object has the following elements :

coefficients: the vector of coefficients,
vcov: the variance–covariance matrix of the coefficients,
residuals: the vector of residuals (these are the residuals of the (quasi-)demeaned model),
weights: (only for weighted estimations) weights as specified,
df.residual: degrees of freedom of the residuals,
formula: an object of class "Formula" describing the model,
model: the model frame as a "pdata.frame" containing the variables used for estimation: the response is in first column followed by the other variables, the individual and time indexes are in the 'index' attribute of model,
ercomp: an object of class "ercomp" providing the estimation of the components of the errors (for random effects models only),
aliased: named logical vector indicating any aliased coefficients which are silently dropped by plm due to linearly dependent terms (see also detect.lindep()),
call: the call.

It has print, summary and print.summary methods. The summary method creates an object of class "summary.plm" that extends the object it is run on with information about (inter alia) F statistic and (adjusted) R-squared of model, standard errors, t–values, and p–values of coefficients, (if supplied) the furnished vcov, see summary.plm() for further details.

Details

plm is a general function for the estimation of linear panel models. It supports the following estimation methods: pooled OLS (model = "pooling"), fixed effects ("within"), random effects ("random"), first–differences ("fd"), and between ("between"). It supports unbalanced panels and two–way effects (although not with all methods).

For random effects models, four estimators of the transformation parameter are available by setting random.method to one of "swar" (Swamy and Arora 1972) (default), "amemiya" (Amemiya 1971) , "walhus" (Wallace and Hussain 1969) , or "nerlove" (Nerlove 1971) (see below for Hausman-Taylor instrumental variable case).

The nested random effect model ((Baltagi et al. 2001) ) is estimated by setting model = "random" and effect = "nested", requiring the data to be indexed by a third index in which the "individual" dimension is nested (see section Examples and the vignette "Estimation of error components models with the plm function".)

For first–difference models, the intercept is maintained (which from a specification viewpoint amounts to allowing for a trend in the levels model). The user can exclude it from the estimated specification the usual way by adding "-1" to the model formula.

Instrumental variables estimation is obtained using two–part formulas, the second part indicating the instrumental variables used. This can be a complete list of instrumental variables or an update of the first part. If, for example, the model is y ~ x1 + x2 + x3, with x1 and x2 endogenous and z1 and z2 external instruments, the model can be estimated with:

formula = y~x1+x2+x3 | x3+z1+z2,
formula = y~x1+x2+x3 | . -x1-x2+z1+z2.

If an instrument variable estimation is requested, argument inst.method selects the instrument variable transformation method:

"bvk" (default) for Balestra and Varadharajan–Krishnakumar (1987) ,
"baltagi" for Baltagi (1981) ,
"am" for Amemiya and MaCurdy (1986) ,
"bms" for Breusch et al. (1989) .

The Hausman–Taylor estimator (Hausman and Taylor 1981) is computed with arguments random.method = "ht", model = "random", inst.method = "baltagi" (the other way with only model = "ht" is deprecated).

See also the vignettes for introductions to model estimations (and more) with examples.

References

Amemiya T (1971). “The Estimation of the Variances in a Variance–Components Model.” International Economic Review, 12, 1–13.

Amemiya T, MaCurdy TE (1986). “Instrumental-Variable Estimation of an Error-Components Model.” Econometrica, 54(4), 869-80.

Balestra P, Varadharajan–Krishnakumar J (1987). “Full Information Estimations of a System of Simultaneous Equations With Error Components.” Econometric Theory, 3, 223–246.

Baltagi BH (1981). “Simultaneous Equations With Error Components.” Journal of Econometrics, 17, 21–49.

Baltagi BH, Song SH, Jung BC (2001). “The unbalanced nested error component regression model.” Journal of Econometrics, 101, 357-381.

Baltagi BH (2013). Econometric Analysis of Panel Data, 5th edition. John Wiley and Sons ltd.

Breusch TS, Mizon GE, Schmidt P (1989). “Efficient Estimation Using Panel Data.” Econometrica, 57(3), 695-700.

Hausman JA, Taylor WE (1981). “Panel Data and Unobservable Individual Effects.” Econometrica, 49, 1377–1398.

Nerlove M (1971). “Further Evidence on the Estimation of Dynamic Economic Relations from a Time–Series of Cross–Sections.” Econometrica, 39, 359–382.

Swamy PAVB, Arora SS (1972). “The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models.” Econometrica, 40, 261–275.

Wallace TD, Hussain A (1969). “The Use of Error Components Models in Combining Cross Section With Time Series Data.” Econometrica, 37(1), 55–72.

Author

Yves Croissant

Examples


data("Produc", package = "plm")
zz <- plm(log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp,
          data = Produc, index = c("state","year"))
summary(zz)
#> Oneway (individual) effect Within Model
#> 
#> Call:
#> plm(formula = log(gsp) ~ log(pcap) + log(pc) + log(emp) + unemp, 
#>     data = Produc, index = c("state", "year"))
#> 
#> Balanced Panel: n = 48, T = 17, N = 816
#> 
#> Residuals:
#>      Min.   1st Qu.    Median   3rd Qu.      Max. 
#> -0.120456 -0.023741 -0.002041  0.018144  0.174718 
#> 
#> Coefficients:
#>              Estimate  Std. Error t-value  Pr(>|t|)    
#> log(pcap) -0.02614965  0.02900158 -0.9017    0.3675    
#> log(pc)    0.29200693  0.02511967 11.6246 < 2.2e-16 ***
#> log(emp)   0.76815947  0.03009174 25.5273 < 2.2e-16 ***
#> unemp     -0.00529774  0.00098873 -5.3582 1.114e-07 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    18.941
#> Residual Sum of Squares: 1.1112
#> R-Squared:      0.94134
#> Adj. R-Squared: 0.93742
#> F-statistic: 3064.81 on 4 and 764 DF, p-value: < 2.22e-16

# replicates some results from Baltagi (2013), table 3.1
data("Grunfeld", package = "plm")
p <- plm(inv ~ value + capital,
         data = Grunfeld, model = "pooling")

wi <- plm(inv ~ value + capital,
          data = Grunfeld, model = "within", effect = "twoways")

swar <- plm(inv ~ value + capital,
            data = Grunfeld, model = "random", effect = "twoways")

amemiya <- plm(inv ~ value + capital,
               data = Grunfeld, model = "random", random.method = "amemiya",
               effect = "twoways")

walhus <- plm(inv ~ value + capital,
              data = Grunfeld, model = "random", random.method = "walhus",
              effect = "twoways")

# summary and summary with a furnished vcov (passed as matrix, 
# as function, and as function with additional argument)
summary(wi)
#> Twoways effects Within Model
#> 
#> Call:
#> plm(formula = inv ~ value + capital, data = Grunfeld, effect = "twoways", 
#>     model = "within")
#> 
#> Balanced Panel: n = 10, T = 20, N = 200
#> 
#> Residuals:
#>      Min.   1st Qu.    Median   3rd Qu.      Max. 
#> -162.6094  -19.4710   -1.2669   19.1277  211.8420 
#> 
#> Coefficients:
#>         Estimate Std. Error t-value  Pr(>|t|)    
#> value   0.117716   0.013751  8.5604 6.653e-15 ***
#> capital 0.357916   0.022719 15.7540 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    1615600
#> Residual Sum of Squares: 452150
#> R-Squared:      0.72015
#> Adj. R-Squared: 0.67047
#> F-statistic: 217.442 on 2 and 169 DF, p-value: < 2.22e-16
summary(wi, vcov = vcovHC(wi))
#> Twoways effects Within Model
#> 
#> Note: Coefficient variance-covariance matrix supplied: vcovHC(wi)
#> 
#> Call:
#> plm(formula = inv ~ value + capital, data = Grunfeld, effect = "twoways", 
#>     model = "within")
#> 
#> Balanced Panel: n = 10, T = 20, N = 200
#> 
#> Residuals:
#>      Min.   1st Qu.    Median   3rd Qu.      Max. 
#> -162.6094  -19.4710   -1.2669   19.1277  211.8420 
#> 
#> Coefficients:
#>         Estimate Std. Error t-value  Pr(>|t|)    
#> value   0.117716   0.009712  12.121 < 2.2e-16 ***
#> capital 0.357916   0.042931   8.337 2.552e-14 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    1615600
#> Residual Sum of Squares: 452150
#> R-Squared:      0.72015
#> Adj. R-Squared: 0.67047
#> F-statistic: 74.6338 on 2 and 9 DF, p-value: 2.4936e-06
summary(wi, vcov = vcovHC)
#> Twoways effects Within Model
#> 
#> Note: Coefficient variance-covariance matrix supplied: vcovHC
#> 
#> Call:
#> plm(formula = inv ~ value + capital, data = Grunfeld, effect = "twoways", 
#>     model = "within")
#> 
#> Balanced Panel: n = 10, T = 20, N = 200
#> 
#> Residuals:
#>      Min.   1st Qu.    Median   3rd Qu.      Max. 
#> -162.6094  -19.4710   -1.2669   19.1277  211.8420 
#> 
#> Coefficients:
#>         Estimate Std. Error t-value  Pr(>|t|)    
#> value   0.117716   0.009712  12.121 < 2.2e-16 ***
#> capital 0.357916   0.042931   8.337 2.552e-14 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    1615600
#> Residual Sum of Squares: 452150
#> R-Squared:      0.72015
#> Adj. R-Squared: 0.67047
#> F-statistic: 74.6338 on 2 and 9 DF, p-value: 2.4936e-06
summary(wi, vcov = function(x) vcovHC(x, method = "white2"))
#> Twoways effects Within Model
#> 
#> Note: Coefficient variance-covariance matrix supplied: function(x) vcovHC(x, method = "white2")
#> 
#> Call:
#> plm(formula = inv ~ value + capital, data = Grunfeld, effect = "twoways", 
#>     model = "within")
#> 
#> Balanced Panel: n = 10, T = 20, N = 200
#> 
#> Residuals:
#>      Min.   1st Qu.    Median   3rd Qu.      Max. 
#> -162.6094  -19.4710   -1.2669   19.1277  211.8420 
#> 
#> Coefficients:
#>         Estimate Std. Error t-value  Pr(>|t|)    
#> value    0.11772    0.01881  6.2582 3.095e-09 ***
#> capital  0.35792    0.03178 11.2622 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    1615600
#> Residual Sum of Squares: 452150
#> R-Squared:      0.72015
#> Adj. R-Squared: 0.67047
#> F-statistic: 102.013 on 2 and 9 DF, p-value: 6.5484e-07


## nested random effect model
# replicate Baltagi/Song/Jung (2001), p. 378 (table 6), columns SA, WH
# == Baltagi (2013), pp. 204-205
data("Produc", package = "plm")
pProduc <- pdata.frame(Produc, index = c("state", "year", "region"))
form <- log(gsp) ~ log(pc) + log(emp) + log(hwy) + log(water) + log(util) + unemp
summary(plm(form, data = pProduc, model = "random", effect = "nested"))
#> Nested effects Random Effect Model 
#>    (Swamy-Arora's transformation)
#> 
#> Call:
#> plm(formula = form, data = pProduc, effect = "nested", model = "random")
#> 
#> Balanced Panel: n = 48, T = 17, N = 816
#> 
#> Effects:
#>                    var  std.dev share
#> idiosyncratic 0.001352 0.036765 0.191
#> individual    0.004278 0.065410 0.604
#> group         0.001455 0.038148 0.205
#> theta:
#>             Min.   1st Qu.     Median       Mean    3rd Qu.       Max.
#> id    0.86492676 0.8649268 0.86492676 0.86492676 0.86492676 0.86492676
#> group 0.03960556 0.0466931 0.05713605 0.05577645 0.06458029 0.06458029
#> 
#> Residuals:
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> -1.06e-01 -2.48e-02 -1.82e-03 -5.43e-05  1.98e-02  1.83e-01 
#> 
#> Coefficients:
#>                Estimate  Std. Error z-value  Pr(>|z|)    
#> (Intercept)  2.08921088  0.14570204 14.3389 < 2.2e-16 ***
#> log(pc)      0.27412419  0.02054440 13.3430 < 2.2e-16 ***
#> log(emp)     0.73983766  0.02575046 28.7311 < 2.2e-16 ***
#> log(hwy)     0.07273624  0.02202509  3.3024 0.0009585 ***
#> log(water)   0.07645327  0.01385767  5.5170 3.448e-08 ***
#> log(util)   -0.09437398  0.01677289 -5.6266 1.838e-08 ***
#> unemp       -0.00616304  0.00090331 -6.8227 8.933e-12 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    43.035
#> Residual Sum of Squares: 1.1245
#> R-Squared:      0.97387
#> Adj. R-Squared: 0.97368
#> Chisq: 20213.5 on 6 DF, p-value: < 2.22e-16
summary(plm(form, data = pProduc, model = "random", effect = "nested",
            random.method = "walhus"))
#> Nested effects Random Effect Model 
#>    (Wallace-Hussain's transformation)
#> 
#> Call:
#> plm(formula = form, data = pProduc, effect = "nested", model = "random", 
#>     random.method = "walhus")
#> 
#> Balanced Panel: n = 48, T = 17, N = 816
#> 
#> Effects:
#>                    var  std.dev share
#> idiosyncratic 0.001415 0.037617 0.163
#> individual    0.004507 0.067131 0.520
#> group         0.002744 0.052387 0.317
#> theta:
#>             Min.    1st Qu.     Median       Mean    3rd Qu.       Max.
#> id    0.86533240 0.86533240 0.86533240 0.86533240 0.86533240 0.86533240
#> group 0.05409908 0.06154491 0.07179372 0.07023704 0.07867007 0.07867007
#> 
#> Residuals:
#>      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
#> -1.05e-01 -2.47e-02 -1.88e-03 -5.57e-05  1.99e-02  1.82e-01 
#> 
#> Coefficients:
#>                Estimate  Std. Error z-value  Pr(>|z|)    
#> (Intercept)  2.08165186  0.15034855 13.8455 < 2.2e-16 ***
#> log(pc)      0.27256322  0.02093384 13.0202 < 2.2e-16 ***
#> log(emp)     0.74164483  0.02607167 28.4464 < 2.2e-16 ***
#> log(hwy)     0.07493204  0.02234932  3.3528 0.0008001 ***
#> log(water)   0.07639159  0.01386702  5.5089 3.611e-08 ***
#> log(util)   -0.09523031  0.01677247 -5.6778 1.365e-08 ***
#> unemp       -0.00614840  0.00090786 -6.7724 1.267e-11 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    40.423
#> Residual Sum of Squares: 1.1195
#> R-Squared:      0.97231
#> Adj. R-Squared: 0.9721
#> Chisq: 19579.7 on 6 DF, p-value: < 2.22e-16

## Instrumental variable estimations
# replicate Baltagi (2013/2021), p. 133/162, table 7.1
data("Crime", package = "plm")
FE2SLS <- plm(lcrmrte ~ lprbarr + lpolpc + lprbconv + lprbpris + lavgsen +
                ldensity + lwcon + lwtuc + lwtrd + lwfir + lwser + lwmfg + lwfed +
                lwsta + lwloc + lpctymle + lpctmin + region + smsa + factor(year)
              | . - lprbarr - lpolpc + ltaxpc + lmix,
              data = Crime, model = "within")
G2SLS <- update(FE2SLS, model = "random", inst.method = "bvk")
EC2SLS <- update(G2SLS, model = "random", inst.method = "baltagi")

## Hausman-Taylor estimator and Amemiya-MaCurdy estimator
# replicate Baltagi (2005, 2013), table 7.4; Baltagi (2021), table 7.5
data("Wages", package = "plm")
ht <- plm(lwage ~ wks + south + smsa + married + exp + I(exp ^ 2) + 
              bluecol + ind + union + sex + black + ed |
              bluecol + south + smsa + ind + sex + black |
              wks + married + union + exp + I(exp ^ 2), 
          data = Wages, index = 595,
          random.method = "ht", model = "random", inst.method = "baltagi")
summary(ht)
#> Oneway (individual) effect Random Effect Model 
#>    (Hausman-Taylor's transformation)
#> Instrumental variable estimation
#>    (Baltagi's transformation)
#> 
#> Call:
#> plm(formula = lwage ~ wks + south + smsa + married + exp + I(exp^2) + 
#>     bluecol + ind + union + sex + black + ed | bluecol + south + 
#>     smsa + ind + sex + black | wks + married + union + exp + 
#>     I(exp^2), data = Wages, model = "random", random.method = "ht", 
#>     inst.method = "baltagi", index = 595)
#> 
#> Balanced Panel: n = 595, T = 7, N = 4165
#> 
#> Effects:
#>                   var std.dev share
#> idiosyncratic 0.02304 0.15180 0.025
#> individual    0.88699 0.94180 0.975
#> theta: 0.9392
#> 
#> Residuals:
#>       Min.    1st Qu.     Median    3rd Qu.       Max. 
#> -12.643736  -0.466002   0.043285   0.524739  13.340263 
#> 
#> Coefficients:
#>                Estimate  Std. Error z-value  Pr(>|z|)    
#> (Intercept)  2.9127e+00  2.8365e-01 10.2687 < 2.2e-16 ***
#> wks          8.3740e-04  5.9973e-04  1.3963   0.16263    
#> southyes     7.4398e-03  3.1955e-02  0.2328   0.81590    
#> smsayes     -4.1833e-02  1.8958e-02 -2.2066   0.02734 *  
#> marriedyes  -2.9851e-02  1.8980e-02 -1.5728   0.11578    
#> exp          1.1313e-01  2.4710e-03 45.7851 < 2.2e-16 ***
#> I(exp^2)    -4.1886e-04  5.4598e-05 -7.6718 1.696e-14 ***
#> bluecolyes  -2.0705e-02  1.3781e-02 -1.5024   0.13299    
#> ind          1.3604e-02  1.5237e-02  0.8928   0.37196    
#> unionyes     3.2771e-02  1.4908e-02  2.1982   0.02794 *  
#> sexfemale   -1.3092e-01  1.2666e-01 -1.0337   0.30129    
#> blackyes    -2.8575e-01  1.5570e-01 -1.8352   0.06647 .  
#> ed           1.3794e-01  2.1248e-02  6.4919 8.474e-11 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    243.04
#> Residual Sum of Squares: 4163.6
#> R-Squared:      0.60945
#> Adj. R-Squared: 0.60833
#> Chisq: 6891.87 on 12 DF, p-value: < 2.22e-16

am <- plm(lwage ~ wks + south + smsa + married + exp + I(exp ^ 2) + 
              bluecol + ind + union + sex + black + ed |
              bluecol + south + smsa + ind + sex + black |
              wks + married + union + exp + I(exp ^ 2), 
          data = Wages, index = 595,
          random.method = "ht", model = "random", inst.method = "am")
summary(am)
#> Oneway (individual) effect Random Effect Model 
#>    (Hausman-Taylor's transformation)
#> Instrumental variable estimation
#>    (Amemiya-MaCurdy's transformation)
#> 
#> Call:
#> plm(formula = lwage ~ wks + south + smsa + married + exp + I(exp^2) + 
#>     bluecol + ind + union + sex + black + ed | bluecol + south + 
#>     smsa + ind + sex + black | wks + married + union + exp + 
#>     I(exp^2), data = Wages, model = "random", random.method = "ht", 
#>     inst.method = "am", index = 595)
#> 
#> Balanced Panel: n = 595, T = 7, N = 4165
#> 
#> Effects:
#>                   var std.dev share
#> idiosyncratic 0.02304 0.15180 0.025
#> individual    0.88699 0.94180 0.975
#> theta: 0.9392
#> 
#> Residuals:
#>       Min.    1st Qu.     Median    3rd Qu.       Max. 
#> -12.643192  -0.464811   0.043216   0.523598  13.338789 
#> 
#> Coefficients:
#>                Estimate  Std. Error z-value  Pr(>|z|)    
#> (Intercept)  2.9273e+00  2.7513e-01 10.6399 < 2.2e-16 ***
#> wks          8.3806e-04  5.9945e-04  1.3980   0.16210    
#> southyes     7.2818e-03  3.1936e-02  0.2280   0.81964    
#> smsayes     -4.1951e-02  1.8947e-02 -2.2141   0.02682 *  
#> marriedyes  -3.0089e-02  1.8967e-02 -1.5864   0.11266    
#> exp          1.1297e-01  2.4688e-03 45.7584 < 2.2e-16 ***
#> I(exp^2)    -4.2140e-04  5.4554e-05 -7.7244 1.124e-14 ***
#> bluecolyes  -2.0850e-02  1.3765e-02 -1.5147   0.12986    
#> ind          1.3629e-02  1.5229e-02  0.8949   0.37082    
#> unionyes     3.2475e-02  1.4894e-02  2.1804   0.02922 *  
#> sexfemale   -1.3201e-01  1.2660e-01 -1.0427   0.29709    
#> blackyes    -2.8590e-01  1.5549e-01 -1.8388   0.06595 .  
#> ed           1.3720e-01  2.0570e-02  6.6703 2.553e-11 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Total Sum of Squares:    243.04
#> Residual Sum of Squares: 4160.3
#> R-Squared:      0.60948
#> Adj. R-Squared: 0.60835
#> Chisq: 6879.2 on 12 DF, p-value: < 2.22e-16