Alfred DeMaris - Regression with Social Data, Modeling Continuous and Limited Response Variables

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F test, 60, 68–69, 93, 130–131, 249

Factor change, see Multiplicative effect

Factorial, 449

Factoring, of matrix expressions, 482

Faculty salary dataset, 16, 106–108, 110–112,

126–154, 208–210, 216–218

False positive rate, 271–273

Feasible generalized least squares (FGLS)

estimator, see Weighted least squares (WLS)

estimator

Finite population correction, 27–28

First derivative, 30–31, 44–45, 48, 71, 388

First partial derivative, 105, 163–164, 183–184,

188

First-order interaction, 104

Fit, of model, see Empirical consistency

Fitted line, 40–42, 47

Fitted value(s), 46, 187–188, 198. See also

Predicted y scores

Fixed effect(s), 17, 428

Fixed-effects partial likelihood (FEPL) model,

427–428

Fixed-X assumption, 43–45, 70, 86, 197, 320, 492

Focus variable, 134, 143, 147

Follow-up tests, slope homogeneity test, 210

Fractions, 450–451

Frailty model, see Cox regression model, shared

frailty model

Full information maximum likelihood (FIML)

estimates, 296–302

Fully right-censored survival time,

see Right-censored survival time

Function, 454–456

Function, linear, 455–456

Gamma density, 366, 428

Gamma function, 366

Gauss-Newton procedure, 188–190

Generalized event count models, 361

Generalized least squares (GLS) estimator,

see Weighted least squares (WLS) estimator

Generalized linear model (GLM), 4–7, 353

Generalized R

, see R

, generalized

Generalized variance, 222

Global effect of X

, test for, 298–299

Gompertz density, 386, 393

Gompertz model, 408

Goodness of fit, see Empirical consistency

Grand mean, 132

Gravity model of migration, 164

GSS98 dataset, 16, 40, 61–63, 101–104, 170–182

Gumbel distribution, 393–394, 413

Hadamard product, 478

Hat diagonal, 198, 220–223

Hat matrix, 198

Hazard

constant, 388, 437–438

declining, 397, 428–429, 436, 438

function, defined, 387–388

function, for exponential distribution, 388

function, for standard normal distribution,

317–318

function, parameterizing, in discrete-time

analysis, 437–438

model, 387

of an event, 382

of exclusion, 337–343. See also Inverse Mills

ratio (IMR)

rate, average, 391

rates, type-specific, defined, 419–420

ratio, defined, 396

ratio, in Cox model, 398

ratio, in discrete-time analysis, 436–437

Heckit estimator, see Heckman two-step estimator

Heckman two-step estimator, 335–343, 364

Hessian, 255

Heterogeneity, 365, 393. See also Unmeasured

heterogeneity

Heteroscedasticity, 200–208

consequences of, 202

induced by weighting, 211

of error in OLS estimator of Heckman model,

336

tests for, 202–203

vs. unequal error variances across groups, 209

Hierarchical equations, 178

Higher-order term(s), 168, 178, 213–218

Homogeneity assumption, in Poisson regression,

353

Homogeneity-of-variance assumption, logistic

regression, 283

Homoscedasticity assumption, 352. See also

Constant variance assumption

Hosmer-Lemeshow test, 269–270

Hurdle model, 365, 375–378

Hyperplane, 85

Hypothesis testing, 34–37

Hypothetical population, 29, 42

Idempotent matrix, see Matrix, idempotent

Identically distributed random variables, 32, 59

Identification, 87. See also Just-identified model;

Overidentified model

Identity, scalar, 448

Identity link, see Link function

Identity matrix, see Matrix, identity

Identity transformation in GLM, 4–5

Ill-conditioning, see Essential ill-conditioning;

Nonessential ill-conditioning

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Inception of risk, 384–386, 401, 407, 425

Incidental truncation, see Truncation, incidental

Included-variable bias, 12

Independence assumption, in Poisson regression,

353

Independence of events, 19

Independent sampling, 43, 45

Independent variable, 39

Indeterminacy, in y, 257

Index of summation, 457

Indicator variable, see Dummy variable(s)

Indirect effect, 101, 218

Inefficiency, of OLS estimators, 202

Inferences

in competing risks model, 420

in Cox model, 400

in MULR, 92–98

in multinomial logistic regression, 298–299

in Poisson regression, 354

in probit and logit regression, 255–257

in SLR, 58–61

Influence diagnostics, 198, 218–223, 241.

See also Outlier(s); Regression diagnostics

Influential observations, see Influence diagnostics;

Outlier(s); Regression diagnostics

Information matrix, see Hessian

Inmates dataset, 16

Inner product, 477, 488

Inscribed rectangles, 37

Instantaneous rate of change, 45

Integral, 25–26, 37

Interaction, 63, 110, 300

between categorical and continuous predictors,

143–148

between categorical predictors, 134–136

difficulty in estimating, 268

disordinal, 105, 145–148, 285

effect, 104–109, 213, 285

global test for, in quadratic models, 179–180

model, 104–105, 134–135, 143, 462–463

modeling in logistic regression, 282–287

ordinal, 105, 144–145, 285

ordinal vs. disordinal, in logistic regression, 285

with time, 406–409

Intercept, 44, 48, 50–52, 57, 61, 455

Interest category, 78, 127, 131

Interpretation

of coefficients, probit and logit regression,

259–260

of logit model, 264–267

of parameters, censored regression, 327–328

of regression coefficients in the PRM, 354–356

Interrupted spell, see Left truncation

Interval estimation, 33

Interval measurement, 18

Interval-censored Cox model, 432–433, 436–437,

440–442. See also Complementary log-log

model

Interval-censored data, 430–442

Intrinsically linear model, 164

Introductory sociology dataset, 16, 339–342

Invariance property, 31

Invariance to interval length, in interval-censored

Cox model, 433

Invariance to spell number, in multiepisode

models, 429

Inverse Mills ratio (IMR), 317–318, 322. See also

Hazard of exclusion

Inverse, 198, 224, 227, 449. See also Matrix,

inverse of

Inverted U-shaped curvilinear relationship, 169

Iterative algorithm, 188–190

Joint density function, 30, 71

Jth-order polynomial model, 169

Just-identified model, 8. See also Identification;

Overidentified model

Kaplan-Meier estimator, 401–402

Kids dataset, 14, 362–364, 370

Kullback-Leibler divergence, 359–360

Lack-of-fit mean square (MLSF), 68, 112

Lack-of-fit sum of squares (SSLF), 68, 112

Lack-of-fit test, 67–69

Lagrange multiplier test, 397

Lambda, see Hazard of exclusion; Inverse Mills

ratio (IMR)

Large-sample confidence interval for µ,

see Confidence interval for population mean

Latent continuous variable, 11, 361

Latent root, see Eigenvalue

Latent scale, 251, 259–260, 273–274, 283

Latent vector, see Eigenvector

Least squares, see Ordinary least squares (OLS)

Left censoring, 386

Left truncation, 385–386, 389, 401–402, 421,

434–437, 440

Length, of kth time interval, 391

Level of measurement, 17

Leverage, 198, 219–220, 222–223

Life-table method, 389–392

Likelihood function

defined, 30–31

for censored regression model, 327

for complementary log-log model, 261,

376–377

for Cox model, 398–400

for discrete-time data, 431

for linear regression, 71

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for logistic regression, 255–258

for NBRM, 366

for Poisson hurdle model, 376

for PRM, 354

for probit model, 255

for survival data, general, 394

for truncated regression model, 323

for zero-truncated NBRM, 369

for zero-truncated PRM, 362

Likelihood-ratio chi-squared test 255–256, 395,

400–401, 411, 429. See also Model

chi-squared

Likelihood-ratio index, 275, 359, 363

LIMDEP (computer program)

for count-data models, 360–361, 364, 366, 381

for linear regression, 202

for truncated and censored regression, 323,

327, 336, 340, 343

Limited information maximum likelihood (LIML)

estimation, 295–298

Limited response variable, 1

Limiting value, 466–467

Linear

association, 57

combination, 92, 130–131, 197, 484, 488.

See also Logit model

Logit link, see Link function

Logit model, 371, 373, 423, 430–442. See also

Logistic regression model

Log-likelihood function

defined, 31

for discrete-time data, 431–432

for exponential AFT model, 395

for linear regression, 71

for logistic regression, 255

for PRM, 354

for survival data, general, 394

Log-logistic density, 386, 393

Log-odds, of event occurrence, 430

Log-survival time, 396

Logy model, 186

Lower-order component, 168, 178

Main effect, 106, 134, 147, 175

Main effects model, 105–106, 133, 136, 209

Marginal density of y, 366

MATLAB (computer program), 245

Matrix

addition rule, 477–478

algebra, 473–493

centering, 481, 488–489

correlation, see Correlation matrix

defined, 474

determinant of, 198, 222, 224, 483, 486

diagonal, 200–201, 479–480

diagonal of, 198, 227, 477

expressions, rules for, 481–482

hat, see Hat matrix

idempotent, 480, 488

identity, 480

information, see Hessian

inverse of, 483–485. See also Inverse

multiplication rule, 478–479

notation, for multiple linear regression,

197–200

null, 480

of regressor scores, 197

order of, 474

orthogonal, 480–481

partitioned, see Partitioned matrix

rank of, 240, 484–485

singular, 87

square, 477

subtraction rule, 477–478

symmetric, 480, 486, 488

trace of, 226, 477, 486

transpose of, 474–476

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Maximum likelihood estimation, see also

Estimation; Ordinary least squares (OLS);

Partial likelihood estimation

defined, 30–32

for censored regression model, 326–327

for discrete-time survival model, 430–432,

439–440

for exponential AFT model, 394–395

for linear regression, 70–72

for multinomial logistic regression,

295–297

for NBRM, 366

for Poisson hurdle model, 376

for PRM, 354

for probit and logit models, 254–255

for sample selection model, 335–336

for truncated regression model, 322–323

for zero-truncated NBRM, 369

for ZINB model, 372

for ZIP model, 371

Maximum likelihood estimator (MLE), of the

population mean, 31

May-Hosmer goodness-of-fit test, see Empirical

consistency in Cox model

McDonald-Moffitt decomposition, 328, 330,

332–333

Mean

contrast, 129–131, 140

difference, 132–133

function(s), sample selection model, 334

of residuals, 64

of sample slope in SLR, 58–60

predicted probability, 357–358, 374–375.

See also Predicted probability; Probability,

estimating

square regression (MSR), 93

squared deviation, 26

squared error (MSE) in linear regression,

54–56, 87–88

squared error of an estimator (MSQE), 231

structure, 250, 352

substitution, 230

Mechanism, 101

Mediation, 98–99, 101–104

Metrics, changing, 77

Minimization, of SSE, 48–50, 72, 87

Minority women dataset, 15, 376–378

Misspecification, 203, 211

Mixed second partial derivative, 49, 471

Model chi-squared, 298, 354, 356. See also

Likelihood-ratio chi-squared test

Model comparison, using crossproduct terms,

151–152

Model fit, see Empirical consistency

Model invariance to event type, test for, 420–421,

423

Model misspecification, estimate of σ under, 220

Model-reality consistency, see Authenticity

Moderator variable, 104, 134

Monotonic relationship, 169

Multicategory variable, 128–129

Multicollinearity, see also Collinearity

consequences of, 226–228

diagnosis of, 228–231

in generalized linear models, 241–242

in Heckman model, 337

in logistic regression, 267–268

in polynomial models, 170

problems with, 87, 92, 106, 109–110, 485

remedies for, 110, 231–242

Multiepisode model, 424–429, 440–442

Multinomial logistic regression model, 295,

439–441. See also Unordered categorical

variables

Multiple correlation coefficient, see Coefficient of

determination; Discriminatory power; R

Multiple linear regression (MULR) model, 84–85,

489–493. See also Linear regression model;

Simple linear regression (SLR) model

Multiplication of matrices, see Matrix,

multiplication rule

Multiplicative effect, 187, 264–266, 285–286, 355

Multistate model, 419–424. See also Competing

risks

Naïve model, 257

National Survey of Families and Households

(NSFH), 14

Near linear dependency, 224–225, 227

Negative binomial density, 350–352, 366

Negative binomial regression model (NBRM),

365–366

Negative contagion, 353

Negative signs, rules for, 449

Nested chi-squared test

for binary response models, 256–257, 260, 263

for Cox model, 400, 408, 411

for discrete-time analysis, 437–438

for exponential AFT model, 395

for hurdle model vs. PRM, 376–378

for multiepisode model, 429

for multinomial logistic regression, 299

for overdispersion, 366, 369

for PRM, 354

for ZIP vs. ZINB models, 373

Nested F test

for ANOVA and ANCOVA models, 135, 140,

147, 152

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for multiple regression model, 93–96

for quadratic model, 173, 179–180

for WOLS, 212–213

in omitted-variable bias example, 216–217

Nested model(s), 93, 173–174, 437

No-intercept model, see Regression through the

origin

Nominal measurement, 17

Nonconstant variance, 63–64, 186

Nonessential ill-conditioning, 109

Nonindependence, 293, 297, 426–429

Noninformative censoring, see Censoring,

noninformative

Nonlinear

association, detecting, 113–118

equations, 255

function, 165–170, 455–456

interaction, 104, 177–184

least squares, 165, 184–190

model, estimation of, 188–190

probability model, 251

regression, 184–190

transformation, 110

Nonlinearity

defined, 162–165

in functional form of relationship between y

and x, 162–163

in regressors, modeling in logistic regression,

287–290

in relationship between y and x, 65–66

in the parameters, 86

in the relationship between regressor and

criterion, 109

in x, 163

of model, 162–165

revealed by scatterplot, 171–172

testing for, in logistic regression, 288–290

Nonnested models, comparing, see Vuong test

Nonparametric estimation, 389–393

Nonprobability sample, 26–27, 29

Nonproportionality, 406–410

Normal density, 23–24, 71, 314–343

Normal equations, 49–50, 54, 72, 87, 188, 492

Normal vector, see Vector, normal

Normality assumption, 43, 45, 63, 87, 148,

153–154, 187

Normit link, see Link function

Null hypothesis, 34

Null likelihood, see Likelihood function for

logistic regression

Null matrix, see Matrix, null

Numerical problems, in logistic regression,

267–269

NVAWS, 15

Odds, 264–266, 294–295

Odds ratio(s), 264–267, 301–302

Off-diagonal elements, of Z′Z, 199

Offset, 354

Omitted group, 78, 127

Omitted interaction, 213

Omitted variable, 80

Omitted-variable bias, 80, 98–104, 213–218, 322,

334, 338

Oneway ANOVA model, 129, 132

Optimal distribution, 108–109

Order, of a matrix, see Matrix, order of

Ordered categorical variables, 303–308

Ordered logit model, 305. See also Proportional

odds model

Ordinal interaction, see Interaction, ordinal

Ordinal variable, 18, 40

Ordinary least squares (OLS), 4, 29–30, 45–52,

87, 127, 130. See also Estimation; Maximum

likelihood estimation; Partial likelihood

estimation

alternatives to, under multicollinearity,

231–242

for censored regression, 325, 327

for count-data models, 349, 352–353, 356–357

for nonlinear model, 186, 189–190

for sample selection model, 336, 338–343

for truncated regression, 322–324

solution in matrix notation, 474, 492

unweighted, 211–212

Orthogonal regressors, 79, 228

Orthogonality condition, 11, 45, 64–65, 86, 98, 188

Orthogonality of vectors, 481

Orthonormal set of vectors, 481

Outcome variable, see Dependent variable

Outer product, 477

Outlier(s), 66, 112, 219–221. See also Influence

diagnostics; Regression diagnostics

Overdispersion, see also Equidispersion

defined, 351

diagnostic for, 360

in ZIP model, 372

models accounting for, 364–378

parameter, 366

test for, 360–361, 366, 369, 374

Overidentified model, 8. See also Identification;

Just-identified model

Parallel curves, 178

Parameter(s), 3, 24, 27, 37, 42

Parameter invariance, test for, 409–410

Parameter space, 34

Parametric form, for hazard function, 392–393

Parent model, 93

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Part correlation, see Semipartial correlation

coefficient

Partial correlation coefficient, 89, 115–118

Partial derivative, 86, 259–260, 263, 470–472

Partial effect, 104–108, 134–135, 147–148, 152.

See also Partial regression coefficient, in

two-regressor model; Partial slope

Partial F test, see Nested F test

Partial likelihood estimation, 398–400, 408–409.

See also Estimation; Maximum likelihood

estimation; Ordinary least squares (OLS)

Partial likelihood function, see Likelihood

function for Cox model

Partial likelihood-ratio test, see Likelihood-ratio

chi-squared test

Partial regression coefficient, in two-regressor

model, 123. See also Partial effect; Partial

slope

Partial regression leverage plot, 113–118, 171

Partial slope in interaction model, test of, see Test

of significance of b

+ gz

Partial slope, 176–177, 180–182, 259–260,

462–463. See also Partial effect; Partial

regression coefficient, in two-regressor model

Partialling, 114–115, 168

Partially standardized coefficients, in logistic

regression, 267

Partitioned matrix, 214–215, 475

Partitioning a continuous regressor, 171, 288

Path analysis, 101

Path model, 7–9

Pearson correlation coefficient, see Correlation

coefficient

Percent change, 92, 187, 266, 355

Percentile, of t distribution, 61

Perfect linear combination, 57, 87

Person-period data, 432–434

Plim, 32, 99–101

Point estimate, 33

Point-slope form of a line, 455

Pointwise consistent estimators, 202

Poisson density, 6, 22, 349–351

Poisson hurdle model, see Hurdle model

Poisson regression model (PRM), 6, 353

Polynomial model, 169–170, 438

Population, 17, 27–29, 42

Population mean, 25–26

Population parameter, 27, 37

Population R

, see R

, population

Positive linear trend, 46

Positive relationship, 41

Potential response model, 10

Power of a test, 36

Predicted probability, see also Mean predicted

probability; Probability, estimating

binary response models, 250, 258–259

NBRM, 366, 379

PRM, 357, 378–379

zero-truncated NBRM, 369

zero-truncated PRM, 364

ZINB model, 372–373

ZIP model, 371

Predicted survival time, exponential AFT model,

396

Predicted y scores, 50–52, 90. See also Fitted

value(s)

Prediction error, 29, 47–48, 54–55

Predictor, 39

Principal components regression, 231, 239–242, 486

Probabilistic relationship, 43

Probability, 19–20

as a function of the odds, 267

at which individuals are most susceptible, 261

change in, 263, 267

conditional rule for, 362, 388

density function (PDF), see Density function

distribution, 20, 371

estimating, 299–301, 305–307. See also Mean

predicted probability; Predicted probability

limit, see Plim

rule, for integer-valued random variable, 306

rule, in discrete-time analysis, 431

sample, 26–29

Probit link, see Link function

Probit model, 253–254, 329, 336

Product limit estimator, see Kaplan-Meier

estimator

Proportion correctly classified, 271–272

Proportional constraint, in censored regression

model, 329

Proportional hazards model, see Cox regression

model

Proportional hazards, 398

Proportional odds model, 305–307. See also

Ordered logit model

Proportional reduction in error (PRE) measure, 54

Proportionality constant, 305

Proportionate change, 92, 355

Prospective survival data, 383

Pseudo-inverse, 240–241

Pseudo-isolation assumption, see Orthogonality

condition

Pseudo-R

, see Discriminatory power; R

Pure error mean square (MSPE), 67, 112

Pure error sum of squares (SSPE), 67, 112

P-value, 35

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Quadratic

effect, 175, 213, 300

function, 168, 467

model, 68–69, 163, 168–182

model, nonlinear interaction in, 177–182

model, targeted centering in, 290

model, test for adequacy of, 174

relationship, 109

Quasi-complete separation, 268–269

, see also Coefficient of determination;

Discriminatory power

adjusted, 56, 90

analog for censored regression, 328, 330, 332

analog for count-data models, see

Discriminatory power in count-data models

analog for Cox model, 410–411

analog for logistic regression, 258, 273–276

change in, 174

desirable properties of, 273

for exponential model, 188, 190

for LPM, 249

for MULR, 84, 88

for SLR, 54–56

for WLS, 205

generalized, 275–276, 410–411

limitations of, 56–57

population, 320

Random component, of GLM, 4

Random sample, 27, 35

Random variable, 17, 32

Rank, of a matrix, see Matrix, rank of

Rate of change, 465–466

Rate of event occurrence, 387–388

Ratio measurement, 18

Receiver operating characteristic (ROC) curve,

272–273, 293–294

Recurrent event model, see Multiepisode model

Reduced correlation matrix, 240

Reference group, 78, 127

Regression

assumptions, see Assumptions for linear

regression

diagnostics, 218–223. See also Influence

diagnostics; Outlier(s)

function, in truncated population, 322

model, in standardized form, 198–200

model, in survival analysis, 393–411

on principal components, see Principal

components regression

parameter, identification of, 129

sum of squares (RSS), 54

through the origin, 188–189, 361

Regressor, 39, 214–216

Rejection rule, 35

Relative frequency, 19, 27

Relative risk, 266

Reliability, 109

Repeated sampling, 27, 29, 43

Re-scaling, 77

Research hypothesis, 34

Residual(s), 46–47, 112–118, 188

Response surface model, 68

Response variable, see Dependent variable

Retrospective survival data, 383

Retrospective time frame, 103

Reversal, 100

Ridge constant, 232

Ridge estimator, 233

Ridge regression, 231–239

Ridge trace, 234–239

Right-censored survival time, 383–386

Risk, 382

Risk, inception of, see Inception of risk

Risk score, 411

Risk set, 386

Robust estimator of V(b), see Sandwich estimator

Root signs, 451–452

Row vector, see Vector, row

Rstudent, 221

Sample covariance, 459

Sample mean, 459

Sample selection bias, 319, 336–338, 364

Sample selection model, 333–343. See also

Truncation, incidental

Sample statistic, 27

Sample variance, 458

Sampling distribution, 26–29, 31–33, 58–61

Sampling weights, 211–213

Sampling without replacement, 27

Sampling zero, 370

Sandwich estimator, 427

SAS (computer program)

for binary response models, 257, 263, 267–269,

275, 280

for logistic regression, 292, 296, 298, 305, 307,

310–311

for MULR, 112, 190, 205, 221, 228, 241, 245

for PRM, 354

for reading data, 13

for SLR, 68, 75

for survival analysis, 391, 393, 399, 401–403,

405, 427, 439–440

for truncated and censored regression, 327, 330

Saturated model, 8, 136

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Scalar property, for matrices, 481

Scaled generalized R

, see R

analog for logistic

regression

Scatterplot

for exponential model, 184–186

for mean of y against deciles of x, 172

for revealing nonconstant error variance,

203–204

in MULR, 112–117

in SLR, 39–42, 46–47, 63–67

Scobit model, 260–261

Score test, for proportional odds assumption, 305

Secant line, 465

Second partial derivative, 49, 163, 470–472

Second partials test, 49

Second-order interaction model, 104–105

Second-order polynomial equation, 168–169

Segment I curve, 165–168, 172, 176

Segment II curve, 165, 167–168

Segment III curve, 165, 167–168

Segment IV curve, 166–168

Selection bias, see Sample selection bias

Selection equation, 333, 335, 337, 339–343

Selection propensity, 320, 333, 335

Self-selection, 319, 334

Semiparametric model, see Cox regression model

Semipartial correlation coefficient, 89

Sensitivity, 271–273

Shape of curves, similarity of, 178–179

Shared unmeasured risk factors (SURF) model, 424

Simple linear regression (SLR) model, 43–44,

186–187. See also Linear regression model;

Multiple linear regression (MULR) model

Simple random sample, 27

Simpson’s paradox, 100

Simulation, to create truncated and censored data,

319–320

Simultaneous equations, 48

Singular matrix, see Matrix, singular

Skew, 40–43

Slope, 42–45, 48–52, 58–61

common, 137

constant, 163, 467

equality of, see Coefficient differences, test for

equivalent tests for, 60

homogeneity, test for, 208–210

in SLR, as weighted sum of the y

, 59–60

nonconstant, 467

of a linear equation, defined, 455

of simple linear regression function, 466–467

standardized, see Standardized slope

Slutsky theorem, 11, 32, 56, 99

Specificity, 271–273

Spectral decomposition, 224–225, 227, 240, 486

Spell, see Episode

SPSS (computer program), 13, 68, 75

Spuriousness, 98–104, 109

Square matrix, see Matrix, square

Squared partial correlation coefficient, 115–118

Standard deviation, 26

Standard error, asymptotically correct, in

Heckman two-step estimator, 343

Standard error of estimate, 220

Standard error of prediction, 221

Standard error of the sample mean, 33

Standard logistic density, 252

Standard logistic distribution, 253–254

Standard normal distribution, 25, 33, 232, 253–254

Standardized

coefficient, 90–91, 106, 109, 118, 229, 232, 267

covariance, 26

estimates, solution for, 200

partial regression coefficient, 90–91

principal components coefficients, 241

residual(s), 66–67, 219

sample regression equation, 57

slope, 57–58, 100, 198

variable scores, 198–199, 232

Standard-score form, 25

Start time, 384

STATA (computer program), 13, 202, 263, 343,

381, 405, 427–428

Statistical control, 80–84

Statistical interaction, see Interaction

Statistical model, 2

Statistical power, 108

Stochastic component of model, 43

Stochastic regressors, 70

Stratified Cox model, 407–410, 427–428

Stratum-specific baseline hazard function, 409

Structural equation model, see Covariance

structure model

Structural part of model, 43, 85

Structural zero, 370, 373–375

Students dataset, 15–16, 39, 88–94, 112–118,

219–220, 222–223, 324, 349, 356–357, 360

Substantive equation, 333, 337–343

Sum of squared errors (SSE), 47–48, 54, 87, 188,

190, 495

Sum of squared residuals, see Sum of squared

errors (SSE)

Sum of squares of coefficient estimates, bias in, 227

Sum of variances, 226, 233

Summation notation, 457–460

Suppression, 100

Survival analysis, defined, 382

Survival function, 402–404, 412

Survival time, 425, 433–434

532 INDEX

bindex.qxd 30.8.04 12:00 Page 532

Swarm of points, 219

Symmetric distribution, 252

Symmetric effect, 104

Symmetric matrix, see Matrix, symmetric

Systematic component of GLM, 4

Systematic variance, 84

t test, 58, 60–61, 93, 96, 152. See also

Two-sample t test

Tangent line, 45, 464–466

Target population, 315, 335

Targeted centering, 210, 286–287, 290, 331–332

Taylor series expansion, 189

Test of linearity, 172–175

Test of significance of b

+ gz, 108, 286–287

Third-order polynomial equation, 169–170

Threshold value, 251

Tied event times, 399–400, 402, 438

Time, calendar, 384

Time, survival, see Survival time

Time intervals, 389–392, 430–437

Time-invariant covariate(s), 433–434

Time-varying covariate(s), 385, 404–411,

433–434, 438

Tobit model, see Censored regression model

Tolerance, 110

Total effect, 101

Total sum of squares (TSS), 53–54

Trace, see Matrix, trace of

Transformation(s), 164, 186, 189, 200

Transformed mean in GLM, 4

Transpose, see Matrix, transpose of

True causal effect, 10

Truncated

density, 315–316

normal distribution, moments of, 316–317

PRM, 362–364

PRM, in hurdle model, 375–376

regression model, 321–324, 326, 329

Truncation, incidental, 319, 320–321, 333–343.