Regression Inference in R - Revision history

Rb: /* F-test 3 ways */

2015-09-05T17:07:21Z

‎F-test 3 ways

Rb at 09:21, 28 August 2015

2015-08-28T09:21:18Z

Rb: /* F-test 3 ways */

2015-08-05T22:45:50Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:45:19Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:44:57Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:43:58Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:43:15Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:37:56Z

‎F-test 3 ways

Rb: /* F-test 3 ways */

2015-08-05T22:36:50Z

‎F-test 3 ways

Rb at 22:34, 5 August 2015

2015-08-05T22:34:30Z

@@ Line 98: / Line 98: @@
        lht1 <- lht(reg_ex2, c("age = 0"," educ = 0"))
-which requires as input the unrestricted model, (here <code>reg_ex2</code>) and the restrictions. Here we have two restrictions, i.e. that the coefficients to the two variables <code>age</code> and <code>educ</code> are 0 and hence both variables irrelevant. You could add more restrictions by adding them into the vector list <code>c(  )</code>.
+which requires as input the unrestricted model, (here <code>reg_ex2</code>) and the restrictions. Here we have two restrictions, i.e. that the coefficients to the two variables <code>age</code> and <code>educ</code> are 0 and hence both variables irrelevant. You could add more restrictions by adding them into the vector list <code>c(  )</code>. Also note that instead of the short version (<code>lht</code>) you could use the slightly longer function name (<code>linearHypothesis</code>). But everything else remains unchanged.
 Look at the output and you will find that it is essentially exactly the same as for the <code>anova</code> function. The <code>lht</code> function is more convenient to use for testing purposes, as you will only need the unrestricted model and then add the restriction. Internally the function will then estimate the restricted model, but you as the user will not see it.

@@ Line 54: / Line 54: @@
      <math>H_0: \beta_{exper} = 0.01; H_A: \beta_{exper} > 0.01</math>
-then we can calculate the relevant test statistic according to:
+Noting that the results for the exper variables are in the 2nd row we can calculate the relevant test statistic according to:
-     t_test = (reg_ex1_sm<source enclose=none>$</source>coefficients[<span style="color:red">2</span>,1]-0.1)/reg_ex1_sm<source enclose=none>$</source>coefficients[<span style="color:red">2</span>,2]
+     t_test = (reg_ex1_sm<source enclose=none>$</source>coefficients[<span style="color:red">2</span>,1]-0.01)/reg_ex1_sm<source enclose=none>$</source>coefficients[<span style="color:red">2</span>,2]
-where we recognise that that the experience coefficient is saved in the <span style="color:red">2nd</span> row of coefficients. As it turns out the value of this t-test is 1.5755.
+where we recognise that that the experience coefficient is saved in the <span style="color:red">2nd</span> row of coefficients. As it turns out the value of this t-test is 1.5755. Sometime, especially if you have many explanatory variables, it can be awkward to have to count in which row the relevant coefficients are. But you can also use the name of the relevant variable as follows:
 = F-tests =

← Older revision		Revision as of 22:45, 5 August 2015
Line 112:		Line 112:

	Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue">reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown">.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <code><span style="color:red">-age-educ</span></code>.		Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue">reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown">.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <code><span style="color:red">-age-educ</span></code>.
		+
		+	Of course, the results are absolutely identical.

	= p-value =		= p-value =

@@ Line 111: / Line 111: @@
       Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue">reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown">.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <code><span style="color:brown">-age-educ</span></code>.
+Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue">reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown">.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <code><span style="color:red">-age-educ</span></code>.
 = p-value =

@@ Line 100: / Line 100: @@
 The last way to calculate an F-test is by using the <code>waldtest</code> function which is a part of the AER package. In some ways this is the most powerful of the three options, in particular if you also want to allow for heteroskedastic error terms (see [[R_robust_se]]). All you need to do to calculate the above F-test is to call the following line
-      > waldtest(<span style="color:blue>reg_ex2</span>, <span style="color:brown>.~.</span> <span style="color:red>- age - educ</span>)
+      > waldtest(<span style="color:blue">reg_ex2</span>, <span style="color:brown">.~.</span> <span style="color:red">- age - educ</span>)
       Wald test
@@ Line 111: / Line 111: @@
       Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
-Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue>reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown>.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <span style="color:brown><code>-age-educ</code></span>.
+Don't be confused by the name "waldtest" in the end you get the same F-test. As for the <code>lht</code> function you will only need the unrestricted model (<code><span style="color:blue">reg_ex2</span></code>) as the first input. The second input into the function specifies the restriction to be tested, or more literally specifies how the restricted model should look like relative to the unrestricted one. We start this specification by the term <code><span style="color:brown">.~.</span></code> which basically says "use the same terms to the left and right of the "~" sign, but then remove the age and education variables, <code><span style="color:brown">-age-educ</span></code>.
 = p-value =

← Older revision		Revision as of 22:36, 5 August 2015
Line 98:		Line 98:
	Look at the output and you will find that it is essentially exactly the same as for the <code>anova</code> function. The <code>lht</code> function is more convenient to use for testing purposes, as you will only need the unrestricted model and then add the restriction. Internally the function will then estimate the restricted model, but you as the user will not see it.		Look at the output and you will find that it is essentially exactly the same as for the <code>anova</code> function. The <code>lht</code> function is more convenient to use for testing purposes, as you will only need the unrestricted model and then add the restriction. Internally the function will then estimate the restricted model, but you as the user will not see it.

		+	The last way to calculate an F-test is by using the <code>waldtest</code> function which is a part of the AER package. All you need to do to calculate the above F-test is to call the following line
		+
		+	> waldtest(reg_ex2, .~. - age - educ)
		+	Wald test
		+
		+	Model 1: lwage ~ exper + log(huswage) + age + educ
		+	Model 2: lwage ~ exper + log(huswage)
		+	Res.Df Df F Pr(>F)
		+	1 423
		+	2 425 -2 24.741 6.895e-11 ***
		+	---
		+	Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
		+
		+	Don't be confused by the name "waldtest" in the end you get the same F-test.

	= p-value =		= p-value =

@@ Line 68: / Line 68: @@
      reg_ex2 <- lm(lwage~exper+log(huswage)+age+educ,data=mydata)
      reg_ex2_sm <- summary(reg_ex2)
 Calculating the F-test is now very easy. What we need is a restricted and unrestricted model. We use the function <code>anova</code>:
@@ Line 93: / Line 97: @@
 Look at the output and you will find that it is essentially exactly the same as for the <code>anova</code> function. The <code>lht</code> function is more convenient to use for testing purposes, as you will only need the unrestricted model and then add the restriction. Internally the function will then estimate the restricted model, but you as the user will not see it.
 = p-value =