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 v ariable ? SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R George Mo u nt Data anal y tics ed u cator

Meas u ring " lo y alt y" Is a " latent v ariable " re � ected in the " Brand Lo y alt y" s u r v e y items (" manifest v ariables ")? Ho w man y " dimensions " does it ha v e ? Do an y items not re � ect a dimension ? 1 Hinkin , T . R . (1998). A brief t u torial on the de v elopment of meas u res for u se in s u r v e y q u estionnaires . Organi z ational research methods , 1(1). SURVEY AND MEASUREMENT DEVELOPMENT IN R

Parallel anal y sis & scree plot library(psych) # Parallel analysis fa.parallel(brand_loyalty) SURVEY AND MEASUREMENT DEVELOPMENT IN R

Parallel anal y sis & 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

O u r 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 BL9 0.903 b_loyalty_9_EFA$loadings BL10 0.718 -0.134 Loadings: MR2 MR1 MR3 MR2 MR1 MR3 SS loadings 2.134 1.495 1.406 BL1 0.643 Proportion Var 0.213 0.149 0.141 BL2 0.682 Cumulative Var 0.213 0.363 0.503 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 SURVEY AND MEASUREMENT DEVELOPMENT IN R

EFA : Initial diagnostics # Scree plot -- will not change! scree(brand_loyalty) SURVEY AND MEASUREMENT DEVELOPMENT IN R

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

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 Mo u nt Data anal y tics ed u cator

1 Hinkin , T . R . (1998). A brief t u torial on the de v elopment of meas u res for u se in s u r v e y q u estionnaires . Organi z ational research methods , 1(1). SURVEY AND MEASUREMENT DEVELOPMENT IN R

What makes a strong EFA ? MR1 MR2 MR3 Factor loadings : CS1 0.699 CS2 0.741 Primar y factor loading Interpretation CS3 0.604 < .39 Poor CS4 0.616 0.110 CS5 0.243 0.467 .4 - .49 Fair CS6 0.593 CS7 0.752 .5 - .59 Good CS8 0.787 CS9 0.728 .6 - .69 Ver y Good CS10 0.664 0.212 .7 + E x cellent CS11 0.102 c_sat_11_EFA_3$loadings SURVEY AND MEASUREMENT DEVELOPMENT IN R

What makes a strong EFA ? N u mber of eigen v al u es > 1 = n u mber 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 w e don ' t get these ? MR1 MR2 MR3 Drop poorl y- loading items ... one at a time ! CS1 0.703 library(dplyr) CS2 0.748 CS3 0.590 0.101 # Drop CS11, create csat10 CS4 0.610 0.111 0.101 c_sat_10 <- select(c_sat_11, -CS11) CS5 0.232 0.481 CS6 0.618 # Re-run EFA CS7 0.734 c_sat_10_EFA_3 <- fa(csat_10, nfactors = 3 CS8 0.775 c_sat_10_EFA_3 $loadings CS9 0.738 CS10 0.664 0.209 SURVEY AND MEASUREMENT DEVELOPMENT IN R

What if w e don ' t get these ? Loadings: Re v isit n u mber of factors MR2 MR1 MR3 MR4 # Does a 4-factor model load better? CS1 0.623 0.137 CS2 0.780 c_sat10_EFA_4 <- fa(c_sat_10, nfactors = 4 CS3 0.618 c_sat10_EFA_4$loadings 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 SURVEY AND MEASUREMENT DEVELOPMENT IN R

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 reliabilit y SU R VE Y AN D ME ASU R E ME N T D E VE L OP ME N T IN R George Mo u nt Data anal y tics ed u cator

Three forms of reliabilit y SURVEY AND MEASUREMENT DEVELOPMENT IN R

Assessing internal reliabilit y Internal reliabilit y: is the meas u re consistent w ithin itself ? 1 h � ps :// commons .w ikimedia . org /w iki / File : Reliabilit y_ and _v alidit y. s v g SURVEY AND MEASUREMENT DEVELOPMENT IN R

Split - half reliabilit y Do all parts of the s u r v e y contrib u te eq u all y to meas u rement ? # Split-half reliability of customer satisfaction library(psych) splitHalf(c_satisfaction) SURVEY AND MEASUREMENT DEVELOPMENT IN R

Interpreting split - half reliabilit y Look for a v erage > .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 reliabilit y: common meas u res Coe � cient / Cronbach ' s alpha : are all items consistent meas u res of the constr u ct ? # 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

Meas u ring internal reliabilit y R u les of th u mb ( split - half or Cronbach / coe � cient ): Val u e Interpretation <.6 Unacceptable . Items ma y not be meas u ring the same constr u ct . Drop items . .6 to .64 Undesirable .65 to .69 Minimall y acceptable .7 to .79 Respectable .8 to .89 Ver y good .9 > Items ma y be too alike / m u lticollinear . Drop items . SURVEY AND MEASUREMENT DEVELOPMENT IN R

Internal reliabilit y in the meas u rement process Do this a � er EFA diagnostics ! 1 Hinkin , T . R . (1998). A brief t u torial on the de v elopment of meas u res for u se in s u r v e y q u estionnaires . Organi z ational research methods , 1(1). SURVEY AND MEASUREMENT DEVELOPMENT IN R

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