What is a latent v ariable ? SU R VE Y AN D ME ASU R E ME N T D E - - PowerPoint PPT Presentation

What is a latent variable?

SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R

George Mount

Data analytics educator

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Measuring "loyalty"

Is a "latent variable" reected in the "Brand Loyalty" survey items ("manifest variables")? How many "dimensions" does it have? Do any items not reect a dimension?

Hinkin, T. R. (1998). A brief tutorial on the development of measures for use in survey questionnaires. Organizational research methods, 1(1).

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SURVEY AND MEASUREMENT DEVELOPMENT IN R

Parallel analysis & scree plot

library(psych) # Parallel analysis fa.parallel(brand_loyalty)

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Parallel analysis & scree plot

library(psych) # Parallel analysis fa.parallel(brand_loyalty) Parallel analysis suggests that the number of factors = 3 and the number of components = 2

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Our initial EFA

b_loyalty_9_EFA <- fa(brand_loyalty, nfactors = 3) str(b_loyalty_9_EFA) chr [1:51] "residual" "dof" "chi" "nh" "rms" "EPVAL" "crms" "EBIC" "ESABIC" "fit" "fit.off" "sd" "factors" ...

SURVEY AND MEASUREMENT DEVELOPMENT IN R

EFA: Initial diagnostics

b_loyalty_9_EFA$loadings Loadings: MR2 MR1 MR3 BL1 0.643 BL2 0.682 BL3 0.700 BL4 0.545 0.124 BL5 0.772 BL6 0.712 BL7 0.643 0.207 -0.114 BL8 0.619 0.165 BL9 0.903 BL10 0.718 -0.134 MR2 MR1 MR3 SS loadings 2.134 1.495 1.406 Proportion Var 0.213 0.149 0.141 Cumulative Var 0.213 0.363 0.503

SURVEY AND MEASUREMENT DEVELOPMENT IN R

EFA: Initial diagnostics

# Scree plot -- will not change! scree(brand_loyalty)

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SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R

EFA & item refinement

SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R

George Mount

Data analytics educator

SURVEY AND MEASUREMENT DEVELOPMENT IN R Hinkin, T. R. (1998). A brief tutorial on the development of measures for use in survey questionnaires. Organizational research methods, 1(1).

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SURVEY AND MEASUREMENT DEVELOPMENT IN R

What makes a strong EFA?

Factor loadings: Primary factor loading Interpretation < .39 Poor .4 - .49 Fair .5 - .59 Good .6 - .69 Very Good .7 + Excellent

c_sat_11_EFA_3$loadings MR1 MR2 MR3 CS1 0.699 CS2 0.741 CS3 0.604 CS4 0.616 0.110 CS5 0.243 0.467 CS6 0.593 CS7 0.752 CS8 0.787 CS9 0.728 CS10 0.664 0.212 CS11 0.102

SURVEY AND MEASUREMENT DEVELOPMENT IN R

What makes a strong EFA?

Number of eigenvalues > 1 = number of factors

c_sat_11_EFA_3$e.values [1] 3.8192575 1.4994979 1.1742464 0.9873115 0.6356614 0.6098439 0.5221825 [8] 0.5007468 0.4600921 0.4291583 0.3490016

SURVEY AND MEASUREMENT DEVELOPMENT IN R

What makes a strong EFA?

Factor score correlations: < .6 ("Not too similar")

c_sat_11_EFA_3$score.cor csat11_EFA3$score.cor [,1] [,2] [,3] [1,] 1.0000000 0.3713636 0.4340072 [2,] 0.3713636 1.0000000 0.2987252 [3,] 0.4340072 0.2987252 1.0000000

SURVEY AND MEASUREMENT DEVELOPMENT IN R

What if we don't get these?

Drop poorly-loading items ... one at a time!

library(dplyr) # Drop CS11, create csat10 c_sat_10 <- select(c_sat_11, -CS11) # Re-run EFA c_sat_10_EFA_3 <- fa(csat_10, nfactors = 3 c_sat_10_EFA_3 $loadings MR1 MR2 MR3 CS1 0.703 CS2 0.748 CS3 0.590 0.101 CS4 0.610 0.111 0.101 CS5 0.232 0.481 CS6 0.618 CS7 0.734 CS8 0.775 CS9 0.738 CS10 0.664 0.209

SURVEY AND MEASUREMENT DEVELOPMENT IN R

What if we don't get these?

Revisit number of factors

# Does a 4-factor model load better? c_sat10_EFA_4 <- fa(c_sat_10, nfactors = 4 c_sat10_EFA_4$loadings Loadings: MR2 MR1 MR3 MR4 CS1 0.623 0.137 CS2 0.780 CS3 0.618 CS4 0.697 CS5 0.519 0.146 CS6 0.127 0.578 CS7 0.763 CS8 0.820 0.107 CS9 0.717 CS10 0.593 0.220 0.156 -0.163

Let's practice!

SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R

Assessing internal reliability

SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R

George Mount

Data analytics educator

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Three forms of reliability

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Assessing internal reliability

Internal reliability: is the measure consistent within itself?

hps://commons.wikimedia.org/wiki/File:Reliability_and_validity.svg

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SURVEY AND MEASUREMENT DEVELOPMENT IN R

Split-half reliability

Do all parts of the survey contribute equally to measurement?

# Split-half reliability of customer satisfaction library(psych) splitHalf(c_satisfaction)

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Interpreting split-half reliability

Look for average > .8

Split half reliabilities Call: splitHalf(r = c_satisfaction) Maximum split half reliability (lambda 4) = 0.87 Guttman lambda 6 = 0.83 Average split half reliability = 0.82 Guttman lambda 3 (alpha) = 0.82 Minimum split half reliability (beta) = 0.69 Average interitem r = 0.31 with median = 0.29

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Internal reliability: common measures

Coecient/Cronbach's alpha: are all items consistent measures of the construct?

# Cronbach/coefficient alpha of customer satisfacion library(psych) c_sat_alpha <- alpha(c_satisfaction)

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Interpreting Cronbach's alpha

summary(c_sat_alpha) Reliability analysis raw_alpha std.alpha G6(smc) average_r S/N ase mean 0.81 0.82 0.83 0.31 4.5 0.015 3.3 sd median_r 0.49 0.29 c_sat_alpha$total$std.alpha 0.8165769

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Measuring internal reliability

Rules of thumb (split-half or Cronbach/coecient): Value Interpretation <.6

• Unacceptable. Items may not be measuring the same construct. Drop items.

.6 to .64 Undesirable .65 to .69 Minimally acceptable .7 to .79 Respectable .8 to .89 Very good .9 > Items may be too alike/multicollinear. Drop items.

SURVEY AND MEASUREMENT DEVELOPMENT IN R

Internal reliability in the measurement process

Do this aer EFA diagnostics!

Hinkin, T. R. (1998). A brief tutorial on the development of measures for use in survey questionnaires. Organizational research methods, 1(1).

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Let's practice!

SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R