Brian S. Everitt A Handbook of Statistical Analyses using SPSS

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Chapter 8 Analysis of Repeated Measures II: Linear Mixed Effects Models; Computer Delivery of Cognitive Behavioral Therapy 8.1 Description of Data The data to be used in this chapter arise from a clinical trial that is described in detail in Proudfoot et al. (2003). The trial was designed to assess the effectiveness of an interactive program using multi-media techniques for the delivery of cognitive behavioral therapy for depressed patients and known as Beating the Blues (BtB). In a randomized controlled trial of the program, patients with depression recruited in primary care were randomized to either the BtB program, or to Treatment as Usual (TAU). The outcome measure used in the trial was the Beck Depression Inventory II (Beck et al., 1996) with higher values indicating more depression. Measurements of this variable were made on five occasions: © 2004 by Chapman & Hall/CRC Press LLC
Prior to treatment Two months after treatment began At 1, 3, and 6 months follow-up, i.e., at 3, 5, and 8 months after treatment The data for 100 patients, 48 in the TAU group and 52 in the BtB group, are shown in Table 8.1. These data are a subset of the original and are used with the kind permission of the organizers of the study, in particular Dr. Judy Proudfoot. The data in Table 8.1 are repeated measures data with time as the single within-subject factor, i.e., they are longitudinal data. They have the following features that are fairly typical of those collected in many clinical trials in psychology and psychiatry: There are a considerable number of missing values caused by patients dropping out of the study (coded 999 in Table 8.1). There are repeated measurements of the outcome taken on each patient post treatment, along with a baseline pre-treatment measurement. There is interest in the effect of more than treatment group on the response; in this case, the effect of duration of illness categorized as whether a patient had been ill for longer than six months (duration = 1) or for less than six months (duration = 0). The question of most interest about these data is whether the BtB program does better than TAU in treating depression. 8.2 Linear Mixed Effects Models Longitudinal data were introduced as a special case of repeated measures in Chapter 7. Such data arise when subjects are measured on the same response variable on several different occasions. Because the repeated measures now arise solely from the passing of time, there is no possibility of randomizing the occasions, and it is this that essentially differentiates longitudinal data from other repeated measure situations arising in psychology and elsewhere. The special structure of longitudinal data make the sphericity condition described in Chapter 7 very difficult to justify. With longitudinal data, it is very unlikely that the measurements taken close to one another in time will have the same degree of correlation as measurements made at more widely spaced time intervals. An analysis of longitudinal data requires application of a model that can represent adequately the average value of the response at any time © 2004 by Chapman & Hall/CRC Press LLC
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A Handbook of Statistical Analyses
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Preface SPSS, standing for Statisti
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Distributors The distributor for SP
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3 Simple Inference for Categorical
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10 Survival Analysis: Sexual Milest
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1. SPSS Base (Manual: SPSS Base 11.
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Display 1.1 Initial SPSS for Window
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Display 1.3 Variable View window of
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three-periods symbol and filling in
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Display 1.6 Opening an existing SPS
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Display 1.8 Typical dialogue box. s
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Transpose… opens a dialogue for s
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Display 1.11 Selecting subsets of c
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A large number of functions are sup
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Display 1.15 Graph procedures demon
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More than one Output Viewer can be
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The Chart Editor facilities are des
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Display 1.19 Syntax Editor showing
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Table 2.1 Lifespans of Rats (in Day
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The test-statistic is where - y 1 a
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For small samples, p-values for the
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Display 2.1 Data View spreadsheet f
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lifespan in days diet Restricted di
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Lifespan in days 1600 1400 1200 100
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Display 2.6 Settings for controllin
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Display 2.8 Generating an independe
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Display 2.10 Generating a Mann-Whit
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Display 2.13 Generating descriptive
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simply because ages were measured o
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Display 2.18 Generating a Wilcoxon
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Husbands' ages (years) 80 70 60 50
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Display 2.24 Generating correlation
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Display 2.26 Fitting a simple linea
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Table 2.4 Motor Vehicle Theft in th
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2.4.5 More on Husbands and Wives: E
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Table 3.1 Belief in the Afterlife B
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make up the table. Most commonly, a
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This is known as a hypergeometric d
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(2) Odds ratio The odds of Variabl
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Display 3.2 Cross-classifying two c
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Odds Ratio for diet (Restricted die
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Display 3.7 Data View spreadsheet f
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Display 3.10 Generating a chi-squar
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20 10 Observed number 30 0 Psychoti
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Chi-Square Tests Value McNemar Test
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Pearson Chi-Square Likelihood Ratio
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Race of defendant found guilty of m
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Estimate ln(Estimate) Std. Error of
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treatment are independent. Estimate
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Table 4.1 Cleaning Cars Sex (1 = ma
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Table 4.2 (continued) Minimum Tempe
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A measure of the fit of the model i
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Display 4.2 Generating the partial
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We specify the dependent variable a
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for the coefficient is given by [0.
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Display 4.7 Setting inclusion and e
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Model 1 2 Model 1 2 Variables Enter
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proportion of variance of the varia
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The final graph shown in Display 4.
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Display 4.12 Generating a scatterpl
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Model 1 Model 1 Model Summary .973a
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Display 4.15 Blocking explanatory v
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1. Residual plot: This is a scatter
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8 6 4 Frequency 10 2 0 2.25 1.75 1.
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a) Latitude January minimum tempera
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Display 4.22 Extending a spreadshee
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Table 4.4 Sulfur Dioxide and Indica
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Table 4.5 Body Fat Content and Age
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Table 5.1 Fecundity of Fruit Flies
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Table 5.3 Female Social Skills Anxi
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There are some advantages (and, unf
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Display 5.1 SPSS spreadsheet contai
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log-odds of survival log-odds of su
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9.4 Exercises 9.4.1 More on the Tit
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Chapter 10 Survival Analysis: Sexua
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Table 10.1 (continued) Times to Fir
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Table 10.2 Times to Completion of t
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To compare the survivor functions b
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10.3 Analysis Using SPSS 10.3.1 Sex
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Display 10.2 Generating Kaplan-Meie
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Survival Analysis for AGESEX Age of
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Display 10.6 Requesting tests for c
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to complete the task. Children rema
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Cases available in analysis Cases d
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Display 10.10 Plotting the predicte
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Display 10.12 Saving results from a
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The smooth lines in the respective
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EFT AGE Display 10.15 Selected outp
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Table 10.3 Heroin Addicts Data Subj
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Table 10.3 (continued) Heroin Addic
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Table 11.1 Crime Rates in the U.S.
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Table 11.2 AIDS Patient’s Evaluat
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that need to be considered. If the
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the analysis is based on the correl
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We assume that the residual terms a
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Correlation Murder Rape Robbery Agg
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Murder Rape Robbery Aggravated assa
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Display 11.6 Saving factor scores.
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Display 11.8 Requesting descriptive
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a) One-factor model Goodness-of-fit
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Raw Rescaled Factor 1 2 3 4 5 6 7 8
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friendly manner doubts about abilit
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Display 11.16 Reproduced covariance
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11.4.2 More on AIDS Patients’Eval
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Table 12.1 Tibetan Skulls Data Skul
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Euclidean distances are the startin
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Fisher showed that the coefficients
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Display 12.2 Declaring a discrimina
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Box's M F Display 12.4 (continued)
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Display 12.6 (continued) Functions
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Original Cross-validated a place wh
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Display 12.10 Requesting a dendrogr
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* * * * * * H I E R A R C H I C A L
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Display 12.14 Declaring a k-means c
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12.4 Exercises Cluster Number of Ca
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Table 12.2 (continued) SIDS Data Gr
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References Agresti, A. (1996) Intro
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Greenhouse, S. W. and Geisser, S. (
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Stevens, J. (1992) Applied Multivar
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