Spatial Survey Data Modeling - Sampling Spatial Units for Agricultural Surveys - page 319

Residuals:
Min 1Q Median 3Q Max
-15.3153 -3.8782 -0.1096 3.7483 12.0911

Coefficients:
Estimate Std. Error t value Pr( > |t|)
(Intercept) 91.5577 0.5601 163.458 < 2e-16 ***

poly(xc, 2)1 29.7940 5.6210 5.301 7.48e-07 ***

poly(xc, 2)2 -163.3911 5.6987 -28.672 < 2e-16 ***

poly(yc, 2)1 -1.1623 5.6987 -0.204 0.839

poly(yc, 2)2 -149.7870 5.6210 -26.648 < 2e-16 ***

---
Signif. codes: 0 ' *** ' 0.001 ' ** ' 0.01 ' * ' 0.05 ' . ' 0.1 '' 1

Residual standard error: 5.601 on 95 degrees of freedom
Multiple R-squared: 0.9442, Adjusted R-squared: 0.9418
F-statistic: 401.6 on 4 and 95 DF, p-value: < 2.2e-16

Note that the function svyglm fits linear and generalized linear models to data
stored in a survey design object. The main difference between svyglm and glm is
in the estimation method. The maximum likelihood method is not used in svyglm
that fits the model by maximizing the HT estimator of the population loglikelihood
(i.e., the pseudolikelihood).
The results are very different for the various sampling designs. As expected, the
parameter estimates for SRS are the same when using either the erroneous com-
mand lm or the appropriate svyglm. Note that the standard errors are different.
The importance of considering the sampling mechanism is evident from the results
obtained with the other sampling schemes.
See Chambers et al. ( 2012 , Chap. 5) for more details about regression analysis
with sample survey data.
However, the linear paradigm is not the only regression analysis method that can
be used in practical applications. For example, the relationship cannot be linear if
there is a strong correlation between a continuous predictor and a proportion,
because the proportion has to be between zero and one. In this case, a transforma-
tion is needed to link the predictor and the proportion. The underlying theory for
these regression models is the same as for linear regression models. There are many
alternatives for the analysis of binary and categorical sample data.
Logistic regression is one of the most commonly used regression methods. The
logistic regression model for a binary response variable y and predictor variables
X ¼

t

ð x 1 x 2 ... x q Þ is

logit pðÞ¼ʲ 0 þ ʲ 1 x k 1 þ ʲ 2 x k 2 þ ...þ ʲ q x kq ; ð 12 : 31 Þ