## Errata in *Richly Parameterized Linear Models: Additive, Time Series, and Spatial Models Using Random Effects*.

Please tell me about any errors you find by sending e-mail to hodge003 at umn.edu. My thanks to these readers for taking the time to find errors and tell me about them (in alphabetical order by surname):

- Maitreyee Bose, David Draper, Ellie Duffy, Chihyun Lee, Miguel Martinez-Beneito, Philip Reiss, Rob Weiss, Hong Zhao

Known errors in the first printing (so far, the only printing):

p. 17, equation 1.6: In the second line of the equation, the matrix G should be G^{-1}.

p. 21, equation (1.16): The farthest right " X " should be " X' ".

p. 27, line 1: "occurence" should be "occurrence".

p. 36, paragraph beginning "Daniels & Kass", last line: "the logit of each θ_{ij} receives a normal prior centered at zero" should be "log{(π/2 + θ_{ij})/(π/2 − θ_{ij})} receives a normal prior centered at zero for each θ_{ij}" -- on checking Daniels & Kass (1999) again, I'm pretty sure they have a typo in the relevant expression (right column, 12 lines down).

p. 37, 7th line from the bottom: In "is a sequence of MCMC draws from the posterior of g(θ)", omit "MCMC". The g(θ_{(b)}) are a sequence of draws from the posterior but they're not a Markov chain and hence not MCMC draws.

p. 62, paragraph beginning "DF(**w**_{1})", 5th line down: β_{0} should be θ_{0}.

p. 67, 6 lines up from the bottom, far right: "Fr this" should be "For this".

p. 68, 4th line of Section 2.2.4, definition of p_{D}: "+" should be "-".

p. 108, 4 lines below equation (4.9): δ_{l} should be δ_{i}.

p. 108, equation (4.10): In the right-most column of the matrix Z, the 3rd row down is " B_{2} "; it should be " B_{3} " (because it's in the 3rd row). Similarly, in the second column from the right, immediately to the left of the vertical partition line, the 3rd row down is " 0_{n2} "; it should be " 0_{n3} " (because it's in the 3rd row).

p. 109, lines 8-9: "correlation" should be "correlated".

p. 112, all three of the bottom 3 lines: v_{kl} should be σ^{2}_{vl}.

p. 130, line 1: "models can used as part" should be "models can be used as part".

p. 131, equation 5.2: Both places where δ_{ij} occurs, it should be (2ν)^{1/2}δ_{ij}.

p. 131, two lines below equation 5.2: "modified Bessel function" should be "modified Bessel function of the second kind".

p. 146, equation 5.21: In both places where it occurs, "+ Z_{R} u_{R}" should be "− Z_{R} u_{R}".

p. 147, 2nd line of text: "u Z_{R} u" should be "u′ Z_{R} u".

p. 147, equation 5.22: In both places where it occurs, "+ Z_{R} u_{R}" should be "− Z_{R} u_{R}", and "u Z_{R} u" should be "u′ Z_{R} u". (Once again illustrating the hazards of cutting and pasting.)

p. 165, the sub-section on improper CAR (ICAR) models: The line "= − 1/σ^{2}_{s} if *i* and *j* are neighbors" doesn't make sense and should be omitted.

p. 212, line 5 from the bottom: V_{n-I+1} should be V_{n-I}

p. 222, paragraph beginning "A full discussion", line 5: "a old style" should be "an old style".

p. 238, 5 lines under equation (11.2): "X_{1} and X_{1}" should be "X_{1} and X_{2}"

p. 253, 2 lines under equation 12.3: θ_{−} and φ_{−} are (N − 1) × 1, not N × 1 as stated.

p. 254, in equations (12.11) and (12.12), the limits of the summations are incorrect. For each sum, "j=1" should be on the bottom and "N-1" on the top, not the other way around as they are in the book. (Hard to imagine how I missed this one.)

p. 254, paragraph beginning "In ..., the conditional variance": In two places, "con__s__trasts" should be "contrasts".

p. 254, 8th line from bottom (last line of last full paragraph): "d_{1}" should be "d_{41}".

p. 272, two lines up from equation 12.24: "Section 6.1" should be "Section 6.2".

p. 282, last line before Section 12.3: "reproduced the phenomena DLM puzzle" should be "reproduced the phenomena that make up the DLM puzzle"

p. 289, equations (13.3) and (13.4): In each equation, the residual sum of squares has an extra closing parenthesis.

p. 307, Section 14.1, 2nd line: "clincal" should be "clinical".

p. 317, 15th line: The sentence beginning "Chapter 17 chapter" should begin "Chapter 17" (omit "chapter" after "17").

p. 317, 2nd line from bottom: The reference to Wedderburn's paper is not in the Reference section. It is "Wedderburn RWM (1976). On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models. Biometrika, 63:27-32."

p. 319, bottom line on the page: This is not an error but rectifies an unclarity. Before the definition of **u**^{*}, add " **Z**^{*} = **Z**Σ_{s}^{0.5} and ".

p. 320, 6th line: "orthonomal" should be "orthonormal".

p. 321, Paragraph beginning "Two comments": In this line, the second instance of "Γ_{c}" should be "Γ′_{c}" (i.e., matrix transpose).

p. 327, mid-page (end of the first paragraph): "as can be seen by comparing the contours of the restricted likelihood and the __free__ terms" (underlining added) should be "as can be seen by comparing the contours of the restricted likelihood and the __mixed__ terms" (underlining won't be there in the next printing).

p. 334, 2nd line from the bottom: In "likelihood (and thus", the opening parenthesis should be deleted.

p. 342, 4th line: "plotted with an linear vertical scale" should be "plotted with a linear vertical scale".

p. 347, Paragraph beginning "This section", 2nd line from bottom, far left: "fixed terms" should be "free terms".

p. 352, paragraph beginning "Finally", last line: "induce" should be "induces".

p. 354, line 4: (sorry, I can't figure out how to get the hat on top of the σ where it belongs) "next-largest change in \hat{σ}_{s}^{2}" should be "next-largest change in \hat{σ}_{e}^{2}"

p. 361, paragraph beginning "Finally", first line: "note that cases j = 1, 2, 4" should be "note that cases j = 1, 3, 4".

p. 363, paragraph beginning "We'll return", 2nd line from bottom of paragraph: "j = 1, 2, 4" should be "j = 1, 3, 4".

p. 367, last line before Section 17.1: "supercede" should be "supersede".

Section 17.1.1, the first several paragraphs of this subsection, from top p. 368 down to and including the paragraph on p. 369 beginning "A sufficient condition": I have now posted a corrected version of this passage, as noted in the Errata Section of the book's main page. Please go back to the book's main page and download the corrected version.

p. 371, paragraph beginning "A large class", last line: Omit ", for which **Γ**_{12} is null".

p. 372, paragraph beginning "Designs satisfying", last line: Omit "with null **Γ**_{12}".

p. 372, paragraph beginning "We have seen examples", first line: Omit the word "an".

p. 373, bottom line, equation (17.14): The rightmost X should be X'.

p. 374, two lines above equation (17.16): The rightmost X should be X'.

p. 375, first line of equation (17.22): The rightmost X should be X'. (You may have noticed a theme here. The hazards of word processing: copy'n'paste propagates your errors.)

Section 17.1.3 on Gaussian processes, p. 376 to 380: I have now posted a corrected version of this section, as noted in the Errata section of the book's main page. Please go back to the book's main page and download the corrected version.

p. 385, paragraph beginning "This leads to a secondary puzzle", lines 2-3: "down and to the right" should be "down and to the left".

Section 17.2.2 on Expedient 2, p. 385 to 394: I have now posted a corrected version of this section, as noted in the Errata section of the book's main page. Please go back to the book's main page and download the corrected version.

p. 398, paragraph beginning "The only way": In the first line of this paragraph, insert the word "obtain" between "and" and "a" so the phrase reads "The only way to increase the design's resolution and obtain a positive [etc.]"

p. 405, 3rd line up before Section 19.1: "Henn & Hodges (2103)" should be "Henn & Hodges (2013)".

p. 406, first line under equation 19.1: "rank**Z**" should be "rank(**Z**)".

p. 407, 7th line up from the bottom: "the sample sizes, the two mean squares, and the prior parameters" should be "the sample sizes and the prior parameters".

p. 410, paragraph beginning "One might reasonably argue", line 5: "error precision σ^{2}" should be "error precision 1/σ^{2}"

p. 423, before the Weisberg (1980) citation (middle of the page): A citation is missing here. Before the Weisberg citation, this new citation should appear: "Wedderburn RWM (1976). On the existence and uniqueness of the maximum likelihood estimates for certain generalized linear models. *Biometrika*, **63**:27-32."

p. 423, after the Weisberg (1980) citation (middle of the page): A citation is missing here, too. After the Weisberg citation, this new citation should appear: "Weisberg S (1983). Comments on a paper by RR Hocking. *Technometrics*, **25**:240-244."

p. 428, right column: After the first entry (for Ward, K.), add a line: "Wedderburn, R.W.M., 317"