Brian S. Everitt A Handbook of Statistical Analyses using SPSS

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Iteration 0 1 2 3 4 5 6 7 8 Update Type Fixed Effects Random Effects Residual Total Intercept TREAT C_MONTH C_PRE Intercept C_MONTH Number of Levels Model Dimension a Covariance Structure Number of Parameters Subject Variables 1 1 1 1 1 1 1 1 1 Identity 1 SUBJECT 1 Identity 1 SUBJECT 1 6 7 a. Dependent Variable: Post-treatment depression score. Number of Step-halvings Iteration History b Covariance Parameters Fixed Effect Parameters Intercept C_MONTH -2 Restricted [subject = [subject = Log SUBJECT] SUBJECT] Likelihood Residual ID diagonal ID diagonal Intercept TREAT C_MONTH C_PRE Initial 0 2021.046 26.14744 26.1474442 26.1474442 16.67599 -5.27073 1.1903886 .5125490 Scoring 1 1964.729 25.43479 41.2184411 2.8328789 16.63831 -4.50924 1.0287282 .5522275 Scoring 1 1926.724 24.90006 49.2784441 6.1882973 16.65211 -3.94426 -.8923691 .5796988 Scoring 1 1900.683 24.52781 52.9800480 3.0078202 16.67899 -3.59681 -.8017594 .5966415 Scoring 0 1875.382 24.04293 55.3249894 3.865E-02 16.71171 -3.20019 -.7000578 .6172862 Scoring 0 1874.882 23.96467 52.7822184 .2091313 16.70738 -3.23882 -.7087159 .6153676 Newton 0 1874.880 23.96393 53.0260027 .2012500 16.70778 -3.23618 -.7081400 .6154884 Newton 0 1874.880 23.96392 53.0277710 .2013409 16.70778 -3.23619 -.7081412 .6154881 Newton 4 1874.880 a 23.96392 53.0277710 .2013409 16.70778 -3.23619 -.7081412 .6154881 a. All convergence criteria are satisfied. b. Dependent Variable: Post-treatment depression score . Parameter Residual Intercept [subject = ID diagonal SC] C_MONTH [subject ID diagonal SC] a. Dependent Variable: Post-treatment depression score . Estimates of Covariance Parameters a 95% Confidence Interval Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound 23.96392 .9905226 8.013 .000 18.7643740 30.6042397 53.02777 .2225126 5.750 .000 37.7106173 74.5663874 .2013409 .2975969 .677 .499 .111200E-02 3.6481403 Display 8.15 Part of random intercept and slope model output for BtB data. The Wald test (Wald z = 0.68, p = 0.5) demonstrates that the variance of the random slope effects is not significantly different from zero and here the simpler random intercept model provides an adequate description of the data. This might be because there is little departure of the observed correlation matrices in each treatment group from the compound symmetry structure allowed by the random intercept model, but it could also be a result of the random slope model we used being too restrictive since it did not allow for a possible correlation between the random intercept and random slope terms. SPSS version 11.0.1 (the one used in this text) does not allow for such a correlation, although version 11.5 and higher will allow this correlation to be a parameter in the model. The final model chosen to describe the average profiles of BDI scores in the two groups over the four post-treatment visits is one that includes © 2004 by Chapman & Hall/CRC Press LLC
Parameter Intercept TREAT C_MONTH C_PRE Estimates of Fixed Effects a 95% Confidence Interval Estimate Std. Error df t Sig. Lower Bound Upper Bound 16.70543 1.1920177 90.623 14.014 .000 14.3375015 19.0733606 -3.22321 1.6303743 90.835 -1.977 .051 -6.4618315 1.540319E-02 -.7039984 .1466745 194.693 -4.800 .000 -.9932734 -.4147235 .6165315 7.63E-02 93.058 8.076 .000 .4649276 .7681355 a. Dependent Variable: Post-treatment depression score . Parameter Residual Intercept [subject ID diagonal SUBJECT] Estimates of Covariance Parameters a a. Dependent Variable: Post-treatment depression score . 95% Confidence Interval Estimate Std. Error Wald Z Sig. Lower Bound Upper Bound 25.22031 2.6180353 9.633 .000 20.5773777 30.9108366 52.72001 9.2000578 5.730 .000 37.4484759 74.2193070 Display 8.16 Parameter estimates of the final model for post-treatment BDI. random intercepts for subjects and fixed effects of month, baseline BDI score and treatment (although this had a p-value slightly above the 5% level). The parameter estimates for this model are shown in Display 8.16. Subject heterogeneity accounts for the majority of the residual variability (estimated intra-class correlation 52.72/(52.72 + 25.22) 100 = 67.6%). Conditional on treatment and visit mean post-treatment, BDI is estimated to increase by 0.62 points for each additional baseline BDI score (95% CI from 0.46 to 0.77 points) and conditional on pre-treatment score and treatment group to decrease 0.7 points each month (CI from 0.41 to 0.99 points). Finally, for a given visit and baseline BDI score the BtB treatment is estimated to decrease the mean BDI score by 3.22 points (CI from 0.015 points increase to 6.5 points decrease). There are a number of residual diagnostics that can be used to check the assumptions of a linear mixed effects model. Here we demonstrate how to assess normality of the random effect terms. Checking out the conditional independence and homogeneity of variance is left as an exercise for the reader (Exercise 8.4.3). The Save… button on the Linear Mixed Effects dialogue box allows the user to save predicted values and residuals (see Display 8.7). We check all three available options in the Save sub-dialogue box. This results in three new variables being added to the Data View spreadsheet after model fitting: participants’ BDI scores predicted on the basis of fixed effects only (fxpred_1), values predicted after including the participants’ estimated random effects (pred_1), and estimates of the errors (resid_1). From these we can calculate estimates of the subject random effects using the formula © 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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Display 5.3 Defining a one-way desi
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Dependent Variable: FECUNDIT Tukey
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Click Simple in the resulting Error
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finger taps per minute Between Grou
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Display 5.13 Defining a one-way des
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5.0 4.0 Mean score 6.0 3.0 2.0 B. r
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the data to assess whether the assu
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Chapter 6 Analysis of Variance II:
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Table 6.2 Data from Slimming Clinic
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When the cells of the design have d
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Dependent Variable: reaction time p
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Display 6.5 Requesting a line chart
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Page 172 and 173: MANUAL Total manual no manual MANUA
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Page 178 and 179: ANCOVA assumes that there is no int
Page 180 and 181: Table 7.1 Field Independence and a
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Page 188 and 189: Within-Subjects Factors Measure: ME
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Page 198 and 199: Table 8.1 A Subset of the Data from
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Page 208 and 209: a) TAU group Baseline depression sc
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Page 234 and 235: Display 9.4 Defining a five-way tab
Page 236 and 237: Display 9.6 Defining a logistic reg
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Page 244 and 245: Step 1 a Table 9.2 LR Test Results
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Page 248 and 249: 9.4 Exercises 9.4.1 More on the Tit
Page 250 and 251: Chapter 10 Survival Analysis: Sexua
Page 252 and 253: Table 10.1 (continued) Times to Fir
Page 254 and 255: Table 10.2 Times to Completion of t
Page 256 and 257: To compare the survivor functions b
Page 258 and 259: 10.3 Analysis Using SPSS 10.3.1 Sex
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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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Brian S. Everitt A Handbook of Statistical Analyses using SPSS

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