Chen Tanghttps://tangc.net/Chen TangSource Themes Academic (https://sourcethemes.com/academic/)en-usCopyright `©` `2020` Chen TangMon, 14 Sep 2020 00:00:00 +0000https://tangc.net/images/icon_hu83723e8c79b0859c5db22398681e0ff2_5565_512x512_fill_lanczos_center_2.pngChen Tanghttps://tangc.net/- Literature timeline: faking in personnel selectionhttps://tangc.net/post/2020-09-13-faking-literature-summary/Mon, 14 Sep 2020 00:00:00 +0000https://tangc.net/post/2020-09-13-faking-literature-summary/<p><em><strong>This is a work in progress, will be finished by the end the September 2020</strong></em></p>
<h2 id="mccrae-and-costa-1983">McCrae and Costa (1983)</h2>
<ul>
<li>Social desirability (SD) is better interpreted as substantial traits than as indicators of response bias</li>
<li>Using SD to correct for response bias should be questioned</li>
</ul>
<h2 id="anderson-warner-and-spencer-1984">Anderson, Warner, and Spencer (1984)</h2>
<ul>
<li>Inflation bias is prevalent and pervasive in employment selection</li>
<li>Inflation bias is negatively correlated with an external performance measure</li>
</ul>
<h2 id="hough-eaton-dunnette-and-kamp-1990">Hough, Eaton, Dunnette, and Kamp (1990)</h2>
<ul>
<li>validities were in the .20s (uncorrected for unreliability or restriction in range) against targeted criterion constructs</li>
<li>Respondents successfully distorted their self-descriptions when instructed to do so</li>
<li>Response validity scales were responsive to different types of distortion</li>
<li>applicants’ responses did not reflect evidence of distortion</li>
<li>validities remained stable regardless of possible distortion by respondents in either unusually positive or
negative directions</li>
</ul>
<h2 id="holden-and-kroner-1992">Holden and Kroner (1992)</h2>
<ul>
<li>Test item response times were statistically adjusted to reflect item latencies in relation both to the person and to the item</li>
<li>Discriminant function analysis indicated that such times could significantly differentiate among standard responding, faking good responses, and faking bad responses</li>
<li>classification hit rates with differential response latencies compared favorably with those rates found with more traditional response dissimulation scales</li>
</ul>
<p>(<em>Note: most of the bullet points were excepts from the papers.</em>)</p>
<h2 id="reference">Reference</h2>
<p>Anderson, C. D., Warner, J. L., & Spencer, C. C. (1984). Inflation bias in self-assessment examinations: Implications for valid employee selection. <em>Journal of Applied Psychology, 69</em>(4), 574-580.</p>
<p>Anglim, J., Lievens, F., Everton, L., Grant, S. L., & Marty, A. (2018). HEXACO personality predicts counterproductive work behavior and organizational citizenship behavior in low-stakes and job applicant contexts. <em>Journal of Research in Personality, 77</em>, 11-20.</p>
<p>Arthur Jr, W., Glaze, R. M., Villado, A. J., & Taylor, J. E. (2010). The magnitude and extent of cheating and response distortion effects on unproctored internet‐based tests of cognitive ability and personality.<em>International Journal of Selection and Assessment, 18</em>(1), 1-16.</p>
<p>Barrick, M. R., & Mount, M. K. (1991). The big five personality dimensions and job performance: A meta-analysis. <em>Personnel Psychology, 44</em>(1), 1-26.</p>
<p>Barrick, M. R., & Mount, M. K. (1996). Effects of impression management and self-deception on the predictive validity of personality constructs. <em>Journal of Applied Psychology, 81</em>(3), 261-272.</p>
<p>Berry, C. M., & Sackett, P. R. (2009). Faking in personnel selection: Tradeoffs in performance versus fairness resulting from two cut‐score strategies. <em>Personnel Psychology, 62</em>(4), 833-863.</p>
<p>Birkeland, S. A., Manson, T. M., Kisamore, J. L., Brannick, M. T., & Smith, M. A. (2006). A meta‐analytic investigation of job applicant faking on personality measures. <em>International Journal of Selection and Assessment, 14</em>(4), 317-335.</p>
<p>Burns, G. N., & Christiansen, N. D. (2011). Methods of measuring faking behavior. <em>Human Performance, 24</em>(4), 358-372.</p>
<p>Böckenholt, U. (2014). Modeling motivated misreports to sensitive survey questions. <em>Psychometrika, 79</em>(3), 515-537.</p>
<p>Cao, M., & Drasgow, F. (2019). Does forcing reduce faking? A meta-analytic review of forced-choice personality measures in high-stakes situations. <em>Journal of Applied Psychology, 104</em>(11), 1347–1368.</p>
<p>Converse, P. D., Peterson, M. H., & Griffith, R. L. (2009). Faking on personality measures: Implications for selection involving multiple predictors. <em>International Journal of Selection and Assessment, 17</em>(1), 47-60.</p>
<p>Cucina, J. M., Vasilopoulos, N. L., Su, C., Busciglio, H. H., Cozma, I., DeCostanza, A. H., … & Shaw, M. N. (2019). The effects of empirical keying of personality measures on faking and criterion-related validity. <em>Journal of Business and Psychology, 34</em>(3), 337-356.</p>
<p>Dwight, S. A., & Donovan, J. J. (2003). Do warnings not to fake reduce faking?. <em>Human Performance, 16</em>(1), 1-23.</p>
<p>Donovan, J. J., Dwight, S. A., & Hurtz, G. M. (2003). An assessment of the prevalence, severity, and verifiability of entry-level applicant faking using the randomized response technique. <em>Human Performance, 16</em>(1), 81-106.</p>
<p>Dunlop, P., Mcneill, I., & Jorritsma, K. (2016). Tailoring the Overclaiming Technique to Capture Faking Behaviour in Applied Settings: A Field Study of Firefighter Applicants. <em>International Journal of Psychology, 51</em>, 792-792. [<em>no fulltext</em>]</p>
<p>Feeney, J. R., & Goffin, R. D. (2015). The overclaiming questionnaire: A good way to measure faking?. <em>Personality and Individual Differences, 82</em>, 248-252.</p>
<p>Ferrando, P. J., & Chico, E. (2001). Detecting dissimulation in personality test scores: A comparison between person-fit indices and detection scales. <em>Educational and Psychological Measurement, 61</em>(6), 997-1012.</p>
<p>Fine, S., & Pirak, M. (2016). Faking fast and slow: Within-person response time latencies for measuring faking in personnel testing. <em>Journal of Business and Psychology, 31</em>(1), 51-64.</p>
<p>Goffin, R. D., & Boyd, A. C. (2009). Faking and personality assessment in personnel selection: Advancing models of faking. <em>Canadian Psychology, 50</em>(3), 151-160.</p>
<p>Griffith, R. L., Chmielowski, T., & Yoshita, Y. (2007). Do applicants fake? An examination of the frequency of applicant faking behavior. <em>Personnel Review, 36</em>(3), 341-355.</p>
<p>Griffith, R. L., Lee, L. M., Peterson, M. H., & Zickar, M. J. (2011). First dates and little white lies: A trait contract classification theory of applicant faking behavior. <em>Human Performance, 24</em>(4), 338-357.</p>
<p>Griffith, R. L., & Peterson, M. H. (2011). One piece at a time: The puzzle of applicant faking and a call for theory. <em>Human Performance, 24</em>(4), 291-301.</p>
<p>Hogan, J., Barrett, P., & Hogan, R. (2007). Personality measurement, faking, and employment selection. <em>Journal of Applied Psychology, 92</em>(5), 1270-1285.</p>
<p>Holden, R. R., & Kroner, D. G. (1992). Relative efficacy of differential response latencies for detecting faking on a self-report measure of psychopathology. <em>Psychological Assessment, 4</em>(2), 170–173.</p>
<p>Holden, R. R., Wood, L. L., & Tomashewski, L. (2001). Do response time limitations counteract the effect of faking on personality inventory validity? <em>Journal of Personality and Social Psychology, 81</em>(1), 160–169.</p>
<p>Hough, L. M. (1998). Effects of intentional distortion in personality measurement and evaluation of suggested palliatives. <em>Human Performance, 11</em>(2-3), 209-244.</p>
<p>Hough, L. M., Eaton, N. K., Dunnette, M. D., Kamp, J. D., & McCloy, R. A. (1990). Criterion-related validities of personality constructs and the effect of response distortion on those validities. <em>Journal of Applied Psychology, 75</em>(5), 581–595.</p>
<p>Jackson, D. N., Wroblewski, V. R., & Ashton, M. C. (2000). The impact of faking on employment tests: Does forced choice offer a solution?. <em>Human Performance, 13</em>(4), 371-388.</p>
<p>Kluger, A. N., & Colella, A. (1993). Beyond the mean bias: The effect of warning against faking on biodata item variances. <em>Personnel Psychology, 46</em>(4), 763-780.</p>
<p>König, C. J., Merz, A. S., & Trauffer, N. (2012). What is in applicants’ minds when they fill out a personality test? Insights from a qualitative study. International Journal of Selection and Assessment, 20(4), 442-452.</p>
<p>Komar, S., Brown, D. J., Komar, J. A., & Robie, C. (2008). Faking and the validity of conscientiousness: A Monte Carlo investigation. <em>Journal of Applied Psychology, 93</em>(1), 140-154.</p>
<p>Kuncel, N. R., & Borneman, M. J. (2007). Toward a new method of detecting deliberately faked personality tests: The use of idiosyncratic item responses. <em>International Journal of Selection and Assessment, 15</em>(2), 220-231.</p>
<p>Levashina, J., & Campion, M. A. (2007). Measuring faking in the employment interview: development and validation of an interview faking behavior scale. <em>Journal of Applied Psychology, 92</em>(6), 1638-1656.</p>
<p>Marcus, B. (2009). ‘Faking’From the Applicant’s Perspective: A theory of self‐presentation in personnel selection settings. <em>International Journal of Selection and Assessment, 17</em>(4), 417-430.</p>
<p>McCrae, R. R., & Costa, P. T. (1983). Social desirability scales: More substance than style. <em>Journal of Consulting and Clinical Psychology, 51</em>(6), 882–888.</p>
<p>McFarland, L. A., & Ryan, A. M. (2006). Toward an integrated model of applicant faking behavior. <em>Journal of Applied Social Psychology, 36</em>(4), 979-1016.</p>
<p>McLarnon, M. J., DeLongchamp, A. C., & Schneider, T. J. (2019). Faking it! Individual differences in types and degrees of faking behavior. <em>Personality and Individual Differences, 138</em>, 88-95.</p>
<p>Meade, A. W., Pappalardo, G., Braddy, P. W., & Fleenor, J. W. (2020). Rapid response measurement: Development of a faking-resistant assessment method for personality. <em>Organizational Research Methods, 23</em>(1), 181-207.</p>
<p>Mueller-Hanson, R. A., Heggestad, E. D., & Thornton, G. C. (2006). Individual differences in impression management: An exploration of the psychological processes underlying faking. <em>Psychology Science, 48</em>(3), 288-312.</p>
<p>Ones, D. S., Viswesvaran, C., & Reiss, A. D. (1996). Role of social desirability in personality testing for personnel selection: The red herring. <em>Journal of Applied Psychology, 81</em>(6), 660-679.</p>
<p>Paulhus, D. L., Harms, P. D., Bruce, M. N., & Lysy, D. C. (2003). The over-claiming technique: Measuring self-enhancement independent of ability. <em>Journal of Personality and Social Psychology, 84</em>(4), 890–904.</p>
<p>Peterson, M. H., Griffith, R. L., Isaacson, J. A., O’Connell, M. S., & Mangos, P. M. (2011). Applicant faking, social desirability, and the prediction of counterproductive work behaviors. <em>Human Performance, 24</em>(3), 270-290.</p>
<p>Piedmont, R. L., McCrae, R. R., Riemann, R., & Angleitner, A. (2000). On the invalidity of validity scales: Evidence from self-reports and observer ratings in volunteer samples. <em>Journal of Personality and Social Psychology, 78</em>(3), 582–593.</p>
<p>Pavlov, G., Maydeu-Olivares, A., & Fairchild, A. J. (2019). Effects of applicant faking on forced-choice and Likert scores. <em>Organizational Research Methods, 22</em>(3), 710-739.</p>
<p>Schermer, J. A., Holden, R. R., & Krammer, G. (2019). The general factor of personality is very robust under faking conditions. <em>Personality and Individual Differences, 138</em>, 63-68.</p>
<p>Schmit, M. J., & Ryan, A. M. (1993). The Big Five in personnel selection: Factor structure in applicant and nonapplicant populations. <em>Journal of Applied Psychology, 78</em>(6), 966–974.</p>
<p>Snell, A. F., Sydell, E. J., & Lueke, S. B. (1999). Towards a theory of applicant faking: Integrating studies of deception. <em>Human Resource Management Review, 9</em>(2), 219-242.</p>
<p>Stark, S., Chernyshenko, O. S., Chan, K.-Y., Lee, W. C., & Drasgow, F. (2001). Effects of the testing situation on item responding: Cause for concern. <em>Journal of Applied Psychology, 86</em>(5), 943–953.</p>
<p>Suchotzki, K., Verschuere, B., Van Bockstaele, B., Ben-Shakhar, G., & Crombez, G. (2017). Lying takes time: A meta-analysis on reaction time measures of deception. <em>Psychological Bulletin, 143</em>(4), 428–453.</p>
<p>Viswesvaran, C., & Ones, D. S. (1999). Meta-analyses of fakability estimates: Implications for personality measurement. <em>Educational and Psychological Measurement, 59</em>(2), 197-210.</p>
<p>Zickar, M. J., & Drasgow, F. (1996). Detecting faking on a personality instrument using appropriateness measurement. <em>Applied Psychological Measurement, 20</em>(1), 71-87.</p>
<p>Zickar, M. J., Gibby, R. E., & Robie, C. (2004). Uncovering faking samples in applicant, incumbent, and experimental data sets: An application of mixed-model item response theory. <em>Organizational Research Methods, 7</em>(2), 168-190.</p>
<p>Zickar, M. J., & Robie, C. (1999). Modeling faking good on personality items: An item-level analysis. <em>Journal of Applied Psychology, 84</em>(4), 551-563.</p>
- Applying principles of big data to the workplace and talent analyticshttps://tangc.net/publication/big-data-chapter/Wed, 01 Jul 2020 00:00:00 +0000https://tangc.net/publication/big-data-chapter/<h3 id="cite-this-chapter">Cite this chapter:</h3>
<p>Song, Q. C., Liu, M., Tang, C., & Long, L. F. (2020). Applying principles of big data to the workplace and talent analytics. In S. E. Woo, L. Tay, & R. W. Proctor (Eds.), <em>Big data in psychological research</em> (p. 319–344). American Psychological Association.
<a href="https://doi.org/10.1037/0000193-015" target="_blank" rel="noopener">https://doi.org/10.1037/0000193-015</a></p>
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- Making sense of model generalizability: A tutorial on cross-validation in R and Shinyhttps://tangc.net/publication/cross-val-tutorial/Mon, 01 Jun 2020 00:00:00 +0000https://tangc.net/publication/cross-val-tutorial/<!-- <div class="alert alert-note">
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- Some Basic Linear Algebrahttps://tangc.net/post/2020-01-09-basic-linear-algebra/Thu, 09 Jan 2020 00:00:00 +0000https://tangc.net/post/2020-01-09-basic-linear-algebra/<p>Purely out of curiosity, I’m recently reading
<a href="http://www.deeplearningbook.org/" target="_blank" rel="noopener">the deep learning book</a> (Goodfellow, Bengio, & Courville, 2016). I noticed that Chapter 2 Linear Algebra is a very quick and effective summary of linear algebra. It provides the right amount of linear algebra for deep learning, as well as machine learning and statistics needed for my research. Below are excerpts from the deep learning book all credit goes to Dr. Ian Goodfellow and his colleagues.</p>
<h2 id="scalars-vectors-matrices-and-tensors">Scalars, Vectors, Matrices and Tensors</h2>
<ul>
<li>scalar: just a single number</li>
<li>vector: an array of numbers</li>
<li>matrix: a 2-dimensional array of numbers</li>
<li>tensor: an n-dimensional array of number</li>
</ul>
<h2 id="transpose">Transpose</h2>
<p>The <strong>transpose</strong> of a matrix is the mirror image of the matrix across the main diagonal:</p>
<p>$$A_{i,j}^{\top} = A_{j,i}$$</p>
<p>Transpose of a scalar is itself. Transpose of a column vector is a row vector and vice versa.</p>
<h2 id="multiplication">Multiplication</h2>
<h3 id="matrix-product">Matrix product</h3>
<p>The matrix product of matrices $A$ and $B$ is a third matrix $C$. In order for this product to be defined, $A$ must have the same number of columns as $B$ has rows. If $A$ is of shape $m \times n$ and $B$ is of shape $n \times p$, then $C$ is of shape $m \times p$.</p>
<p>$$C_{i, j} = \sum_k A_{i, k} B_{k, j}$$</p>
<h3 id="element-wise-product-aka-hadamard-product">Element-wise product (aka Hadamard product)</h3>
<p>$$A \odot B$$</p>
<h3 id="dot-product">Dot product</h3>
<p>The dot product between two vectors $x$ and $y$ of the same length is the matrix product $x^\top y$. the matrix product $C$ can be thought of as the dot products of each corresponding row in $A$ and column in $B$.</p>
<h3 id="properties-of-matrix-multiplication">Properties of matrix multiplication</h3>
<ul>
<li>Distributive: $A(B + C)=AB + AC$</li>
<li>Associative: $A(BC) = (AB)C$</li>
<li>Not commutative: $AB = BA$ is not always true</li>
<li>But dot product between two vectors is commutative: $x^\top y = y^\top x$</li>
<li>Transpose of a matrix product: $(AB)^\top = B^\top A^\top$ (this can be used to prove $x^\top y = y^\top x$)</li>
</ul>
<h2 id="identity-and-inverse-matrices">Identity and Inverse Matrices</h2>
<p>Identity matrix: denoted as $I_n$, all its entries along the main diagonal are 1, all the others are zero.</p>
<p>The inverse of $A$, denoted as $A^{-1}$, is defined as the matrix such that</p>
<p>$$A^{-1}A = I_n$$</p>
<h2 id="linear-dependence-and-span">Linear Dependence and Span</h2>
<p>A <strong>linear combination</strong> of some set of vectors ${v^{(1)}, … , v^{(n)}}$ is given by multiplying
each vector $v^{(i)}$ by a corresponding scalar coefficient and adding the results:</p>
<p>$$\sum_i c_iv^{(i)}$$</p>
<p>The <strong>span</strong> of a set of vectors is the set of all points obtainable by linear combination of the original vectors.</p>
<p>Determining whether $Ax = b$ has a solution thus amounts to testing whether b is in the span of the columns of $A$. This particular span is known as the <strong>column space</strong> or the <strong>range</strong> of $A$.</p>
<h2 id="norms">Norms</h2>
<p>Norm is the measure of the size of a vector. The $L^p$ norm is defined as:</p>
<p>$$|x|_p = \Big(\sum_i |x_i|^p\Big)^{\frac{1}{p}}$$</p>
<p>The <strong>Euclidean norm</strong>, or $L^2$ norm, is used very frequently. It is also common to use the squared $L^2$ norm, which is simply $x^{\top} x$.</p>
<p>However squared $L^2$ norm is undesirable because it changes very slowly near the origin. So when it is important to discriminate between values that are exactly zero and values that are very small but nonzero, we could use $L^1$ norm:</p>
<p>$$|x|_1 = \sum_i|x_i|$$</p>
<p><strong>Max norm</strong> is also common, which is defined by the absolute value of the element with the largest magnitude in the vector:</p>
<p>$$|x|_{\infty} = \max_i|x_i|$$</p>
<p>Above norms describe the size of vectors. <strong>Frobenius norm</strong> can measure the size of a matrix:</p>
<p>$$|A|_F = \sqrt{\sum_{i, j} A^2_{i,j}}$$</p>
<p>This is analogous to the $L^2$ norm of a vector.</p>
<p>The dot product of two vectors can be written in terms of norms:</p>
<p>$$x^{\top}y = |x|_2|y|_2\cos{\theta}$$</p>
<p>where $\theta$ is the angle between $x$ and $y$.</p>
<h2 id="special-kinds-of-matrices-and-vectors">Special Kinds of Matrices and Vectors</h2>
<h3 id="diagonal-matrix">Diagonal matrix</h3>
<p>a matrix $D$ is diagonal if and only if $D_{i, j} = 0$ for all $i \ne j$. We write $\text{diag}(v)$ to denote a square diagonal matrix whose diagonal entries are given by the entries of the vector $v$.</p>
<p>Diagonal matrices are interesting because:</p>
<ol>
<li>
<p>Multiplying by a diagonal matrix is very computationally efficient: $\text{diag}(v) x = v \odot x$</p>
</li>
<li>
<p>Inverting a diagonal matrix is easy: $\text{diag}(v)^{-1} = \text{diag}(1/v_1, …, 1/v_n)^{\top}$</p>
</li>
</ol>
<p>Diagonal matrices do not need to be square. For a non-square diagonal matrix $D$, the product $Dx$ will involve scaling each element of $x$, and either concatenating some zeros to the result if $D$ is taller than it is wide, or discarding some of the last elements of the vector if $D$ is wider than it is tall.</p>
<h3 id="symmetric-matrix">Symmetric matrix</h3>
<p>A symmetric matrix is any matrix that is equal to its own transpose:</p>
<p>$$A = A^{\top}$$</p>
<h3 id="unit-vector">Unit vector</h3>
<p>A unit vector is a vector with unit norm:</p>
<p>$$|x|_2 = 1$$</p>
<h3 id="orthogonal-vectors-and-orthogonal-matrices">Orthogonal vectors and orthogonal matrices</h3>
<p>Vector $x$ and vector $y$ are orthogonal to each other if $x^{\top}y = 0$. If the vectors are not only orthogonal but also have unit norm, we call them <strong>orthonormal</strong>.</p>
<p>An orthogonal matrix is a square matrix whose rows are mutually orthonormal and whose columns are mutually orthonormal:</p>
<p>$$A^{\top}A = AA^{\top} = I$$</p>
<p>Orthogonal matrices are of interest because their inverse is very cheap to compute:</p>
<p>$$A^{-1} = A^{\top}$$</p>
<p>Counterintuitively, rows and columns of an orthogonal matrix are not merely orthogonal but fully orthonormal. There is no special term for a matrix whose rows or columns are orthogonal but not orthonormal.</p>
<p>
<a href="https://en.wikipedia.org/wiki/Orthogonal_matrix" target="_blank" rel="noopener">Definition from Wikipedia</a>: “An orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors).”</p>
<p><em>(To be continued…)</em></p>
- Multi-subgroup Pareto-optimal weightinghttps://tangc.net/project/multi-subgroup/Wed, 01 Jan 2020 00:00:00 +0000https://tangc.net/project/multi-subgroup/<p>There are methods in personnel selection that seeks to improve diversity in the hiring outcomes. Among them, one of the most promising methods is Pareto-optimal weighting via the normal boundary intersection algorithm (De Corte et al., 2007). However, this method only assumes one single minority group. What if we have more than one minority groups in the applicant pool? This project is trying to address this question…</p>
<p>This project is in collaboration with
<a href="http://qchelseasong.com/team-head.html" target="_blank" rel="noopener">Chelsea Song</a> and
<a href="https://research-repository.uwa.edu.au/en/persons/serena-wee" target="_blank" rel="noopener">Serena Wee</a>.</p>
- Orthogonalized Criterion Weightinghttps://tangc.net/project/ocw/Wed, 01 Jan 2020 00:00:00 +0000https://tangc.net/project/ocw/<p>In this project, we introduce another Pareto-optimal weighting method that incorporates a priori inputs regarding relative importance of criterion validity (i.e., expected job performance) and diversity in hiring outcomes.</p>
<p>This project is in collaboration with
<a href="https://ler.illinois.edu/about/faculty-staff/faculty/newman-dan/" target="_blank" rel="noopener">Daniel A. Newman</a> and
<a href="http://qchelseasong.com/team-head.html" target="_blank" rel="noopener">Q. Chelsea Song</a>.</p>
- Item-level faking detectionhttps://tangc.net/project/faking-detection/Fri, 01 Nov 2019 00:00:00 +0000https://tangc.net/project/faking-detection/<p>Scholars have argued that faking happens on the item-level (KKuncel & Tellegen, 2001) and has complex patterns (e.g., non-linearity; Kuncel & Borneman, 2007).</p>
<p>In this project, we put this argument directly to test. Specifically, my collaborator
<a href="https://liberalarts.tamu.edu/psychology/profile/bo-zhang/" target="_blank" rel="noopener">Bo Zhang</a> and I trained some supervised learning models to prediction whether an respondent was faking or not based on item-level personality measurement data. Initial results showed support to Kuncel and his colleagues.</p>
- Dandelionhttps://tangc.net/post/2020-09-12-dandelion/Thu, 12 Sep 2019 00:00:00 +0000https://tangc.net/post/2020-09-12-dandelion/<p>My family and I went to Lake of the Woods in Mahomet, IL this weekend. Summer is pretty much done but I found this white fluffy puffy thing standing beside a sidewalk. Looks like it doesn’t want to say goodbye to summer, much like myself… That’s why I snapped a photo of it.</p>
<p><img src="https://i.imgur.com/WjRqczL.jpg?1" alt="dandelion-1"></p>
<p>By the way, there was a ever so slightly wind going on when I was trying to take this photo, making the dandelion constantly shaking. It was getting dark so I had to slow down the shutter speed, but because of the wind, I couldn’t get a sharp image. My wife offered a solution–she gave it a slight pinch ;o)</p>
<p><img src="https://i.imgur.com/j3hEneY.jpg?1" alt="dandelion-2"></p>
- A Very Detailed Bias-Variance Breakdownhttps://tangc.net/post/2019-09-01-bias-variance-breakdown/Sun, 01 Sep 2019 00:00:00 +0000https://tangc.net/post/2019-09-01-bias-variance-breakdown/<p>Although the concept of bias-variance trade-off is often discussed in machine learning textbooks, e.g., Bishop (2006), Hastie, Tibshirani, and Friedman (2009), James et al. (2013), I also find it important in almost any occasions in which we need to fit a statistical model on a data set with a limited number of observations. To better understand the trade-off, we should be clear about the bias-variance decomposition. I prefer to call it bias-variance breakdown cause there are fewer syllables. This post is an attempt to go through the breakdown in a very detailed manner, mainly for my future reference. It may not be 100% correct because I’m very new to this topic. I will make changes if there is anything wrong.</p>
<h2 id="what-is-being-broken-down">What is being broken down?</h2>
<p>First off, the bias-variance concept lives in theory. In practice, we have no way to separate bias and variance. What we could observe is just the sum of them, as well as something called “irreducible error”. We will cover that later in this post.</p>
<p>Since we are talking about theory, let’s make up the thing that needs to be broken down. Let’s assume that we are interested in studying the relationship between $X$ and $Y$. Suppose the relationship is a regression model $Y = f(X) + \epsilon$, $\epsilon$ is i.i.d. $E(\epsilon) = 0$ and $\text{Var}(\epsilon) = \sigma^2$.</p>
<p>Then we obtain a data set, $D$, that has $x_i$ and $y_i$ ($D = {x_i, y_i}$). Note that in the data set, $X$ and $Y$ are lowercase and have subscripts. This is because we are referring to observed data of $X$ and $Y$.</p>
<p>As usual, we fit a model to $D$ and obtain the model $\widehat{f}(x_i)$. There is a “hat” on $f(x_i)$ because we are estimating the true model, $f()$. After getting $\widehat{f}()$, we are interested in how this model would perform in the future. So we have to come up with a way to measure the performance of the model when applied to new data. The most common way to measure the predictive performance of a model is mean squared error (MSE) on a new data set ${x^*, y^*}$, or theoretically, the expected squared error:</p>
<p>$$E[(y^* - \widehat{f}(x^*))^2]$$</p>
<p>This is the thing to be broken down.</p>
<h2 id="breaking-it-down">Breaking it down</h2>
<p>Before we go further, we need to make sure we are clear about which is which. Since this is an expected value, there must be random variables in this equation. What is random here? First, let’s take a look at $\widehat{f}(x^*)$. We know that $\widehat{f}()$ comes from $D$, and $D$ contains $\epsilon$, because the true model we assumed is $Y = f(X) + \epsilon$. So $\widehat{f}()$ also contains $\epsilon$ and hence it is a random variable. Second, what about $y^*$? Since ${x^*, y^*}$ is a sample from the true model, it again contains $\epsilon$, therefore $y^*$ is also a random variable.</p>
<p>Let’s now play a mathematical trick:</p>
<p>$$E[(y^* - \widehat{f}(x^*))^2] = E[(y^* - f(x^*) + f(x^*) - \widehat{f}(x^*))^2]$$</p>
<p>Here we just add and subtract $f(x^*)$, nothing is changed. Let $A = y^* - f(x^*)$ and $B = f(x^*) - \widehat{f}(x^*)$. Then the above equation becomes:</p>
<p>$$
\begin{aligned}
& E[(A + B)^2]\<br>
&= E[A^2 + B^2 + 2AB]\<br>
&= E[A^2] + E[B^2] + 2E[AB]
\end{aligned}
$$</p>
<p>Let’s put $A$ and $B$ back</p>
<p>$$E[(y^* - f(x^*))^2] + E[(f(x^*) - \widehat{f}(x^*))^2] + 2E{[y^* - f(x^*)][f(x^*) - \widehat{f}(x^*)]}$$</p>
<p>This is very complicated, especially the long thing on the right. Let’s first expand it:
$$2{E[y^* f(x^*)] - E[y^* \widehat{f}(x^*)] - E[f(x^*) f(x^*)] + E[f(x^*) \widehat{f}(x^*)]}$$</p>
<p>According to our theoretical model, we know that $y^* = f(x^*) + \epsilon$, so</p>
<p>$$2{E[(f(x^*) + \epsilon) f(x^*)] - E[(f(x^*) + \epsilon) \widehat{f}(x^*)] - E[f(x^*) f(x^*)] + E[f(x^*) \widehat{f}(x^*)]}$$</p>
<p>$$2{[f(x^*)]^2 - E[f(x^*) \widehat{f}(x^*) + \epsilon \widehat{f}(x^*)] - [f(x^*)]^2 + E[f(x^*) \widehat{f}(x^*)]}$$</p>
<p>$$2{[f(x^*)]^2 - E[f(x^*) \widehat{f}(x^*)] + E[\epsilon \widehat{f}(x^*)] - [f(x^*)]^2 + E[f(x^*) \widehat{f}(x^*)]}$$</p>
<p>Four terms cancel out, the term $E[\epsilon \widehat{f}(x^*)] = 0$, because $\epsilon$ and $\widehat{f}(x^*)$ are independent. Therefore $E[\epsilon \widehat{f}(x^*)] = E[\epsilon] \times E[\widehat{f}(x^*)] = 0$.</p>
<p>OK. That long thing becomes zero and we are left with</p>
<p>$$E[(y^* - f(x^*))^2] + E[(f(x^*) - \widehat{f}(x^*))^2]$$</p>
<p>Now let’s play a similar trick on the second term, the first term remains unchanged.</p>
<p>$$E[(y^* - f(x^*))^2] + E{[f(x^*) - E[\widehat{f}(x^*)] + E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$$</p>
<p>Again let $A = f(x^*) - E[\widehat{f}(x^*)]$ and $B = E[\widehat{f}(x^*)] - \widehat{f}(x^*)$.</p>
<p>$$E[(y^* - f(x^*))^2] + E[(A + B)^2]$$</p>
<p>$$E[(y^* - f(x^*))^2] + E[A^2] + E[B^2] + 2E[AB]$$</p>
<p>Plug in $A$ and $B$.</p>
<p>$$E[(y^* - f(x^*))^2] + E{[f(x^*) - E[\widehat{f}(x^*)]]^2} + E{[E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$$
$$ + 2E{[f(x^*) - E[\widehat{f}(x^*)]][E[\widehat{f}(x^*)] - \widehat{f}(x^*)]}$$</p>
<p>Let’s again look at the most annoying thing on the second row. We notice that (1) $f(x^*) - E[\widehat{f}(x^*)]$ is a constant, and (2) the expected value of $E[\widehat{f}(x^*)] - \widehat{f}(x^*)]$ is just $E{E[\widehat{f}(x^*)]} - E[\widehat{f}(x^*)]$. This equals $E[\widehat{f}(x^*)] - E[\widehat{f}(x^*)] = 0$.</p>
<p>So we are left with</p>
<p>$$E[(y^* - f(x^*))^2] + E{[f(x^*) - E[\widehat{f}(x^*)]]^2} + E{[E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$$</p>
<p>We also notice that, in the second term, both $f(x^*)$ and $E[\widehat{f}(x^*)]$ are constants, so we can drop the expectation operator.</p>
<p>$$E[(y^* - f(x^*))^2] + [f(x^*) - E[\widehat{f}(x^*)]]^2 + E{[E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$$</p>
<p>Cool! We have finished the breakdown.</p>
<h2 id="naming-things">Naming things</h2>
<p>As a final step, let’s name the three terms in</p>
<p>$$E[(y^* - f(x^*))^2] + [f(x^*) - E[\widehat{f}(x^*)]]^2 + E{[E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$$</p>
<p>The first term, $E[(y^* - f(x^*))^2]$, is the variance of $\epsilon$, which is $\sigma^2$. We call this “irreducible error” or “irreducible noise”.</p>
<p>The second term, $[f(x^*) - E[\widehat{f}(x^*)]]^2$, is the “squared bias”, because the definition of the bias of an estimator is $\text{bias}(\widehat{\theta}) = E(\widehat{\theta}) - \theta$.</p>
<p>The third term, $E{[E[\widehat{f}(x^*)] - \widehat{f}(x^*)]^2}$is, by definition, the variance of $\widehat{f}(x^*)$.</p>
<p>So to put everything together,</p>
<p>$$E[(y^* - \widehat{f}(x^*))^2] = \text{Var}(\epsilon) + \text{bias}^2(\widehat{f}(x^*)) + \text{Var}(\widehat{f}(x^*))$$</p>
<h2 id="reference">Reference</h2>
<p>Bishop, Christopher M. (2006). <em>Pattern recognition and machine learning</em>. New York: Springer,</p>
<p>Gareth James, Daniela Witten, Trevor Hastie, Robert Tibshirani. (2013). <em>An introduction to statistical learning: with applications in R</em>. New York :Springer,</p>
<p>Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). <em>The elements of statistical learning: data mining, inference, and prediction</em>. 2nd ed. New York: Springer.</p>
- <link>https://tangc.net/cv/</link><pubDate>Mon, 01 Jan 0001 00:00:00 +0000</pubDate><guid>https://tangc.net/cv/</guid><description><h1 id="chen-tang">Chen Tang</h1>
<p><em>(Updated: September 2020, Click
<a href="https://tangc.net/cv.pdf">here</a> to download the PDF version</em></p>
<p>University of Illinois at Urbana-Champaign</p>
<p>504 E Armory Ave, Champaign, IL 61820</p>
<p>
<a href="mailto:chent3@illinois.edu">chent3@illinois.edu</a></p>
<h2 id="education">Education</h2>
<p><strong>School of Labor and Employment Relations, University of Illinois at Urbana-Champaign</strong></p>
<ul>
<li>PhD Student, 2017-Present</li>
</ul>
<p><strong>School of Psychology and Cognitive Science, East China Normal University</strong></p>
<ul>
<li>
<p>M.Ed., Applied Psychology, 2009-2012</p>
</li>
<li>
<p>B.S., Psychology, 2005-2009</p>
</li>
</ul>
<h2 id="research-interests">Research Interests</h2>
<ul>
<li>Personnel selection, diversity in HR</li>
<li>Organizational research methods</li>
<li>People analytics, predictive modeling, data visualization</li>
<li>Individual career development/change, unemployment</li>
</ul>
<h2 id="ongoing-projects">Ongoing Projects</h2>
<p><strong>Tang, C.</strong>, Chen, Y., & Wei, W. (under review). [Details omitted for blind reviewing]. <em>Journal of Business Ethics</em>.</p>
<p><strong>Tang, C.</strong>, & Zhang. B. (writing in progress). Faking is in the details: Improving faking detection accuracy using personality items.</p>
<p><strong>Tang, C.</strong>, Chen, Y., Song, Q. C., & Newman, D. A. (writing in progress). Valuing Diversity in Hiring when Choosing a Predictor Weighting Method: An Extension of Scakett et al. (2017).</p>
<p><strong>Tang, C.</strong>, Shin, H. J., & Song, Q. C. (submitted). [Details omitted for blind reviewing].</p>
<p>Song, Q. C., & <strong>Tang, C</strong>. (data analysis). Adverse impact reduction for multiple subgroups: A Pareto-optimization approach.</p>
<p>Lee, SH., & <strong>Tang, C</strong>. (data collection). A dual-path model of job search behaviors.</p>
<h2 id="publications">Publications</h2>
<p>Song, Q. C., <strong>Tang, C.</strong>, & Wee, S. (in press). Making sense of model generalizability: A tutorial on cross-validation in R and Shiny. <em>Advances in Methods and Practices in Psychological Science</em>.</p>
<p>Yang, Y., <strong>Tang, C.</strong>, Qu, X., Wang, C., & Denson, T. F. (2018). Group facial width-to-height ratio predicts intergroup negotiation outcomes. <em>Frontiers in Psychology</em>.</p>
<p><strong>Tang, C.</strong>, & Yang, Y. (2017). Goals. In Zeigler-Hill, V., & Shackelford, T. K. (Eds.) <em>Encyclopedia of Personality and Individual Difference</em>. Springer.</p>
<h2 id="conference-presentations">Conference Presentations</h2>
<p><strong>Tang, C.</strong>, Chen, Y., Wei, W. (August 2020). External Work Locus of Control and Unethical Pro-Organizational Behavior: A Dual-Path Model [Paper]. 80th Annual Meeting of the Academy of Management, Vancouver, British Columbia, Canada. (Conference canceled)</p>
<p><strong>Tang, C.</strong>, Newman, D. A., & Song, Q. C. (April 2020). Addressing diversity-Validity trade-offs via Pareto weights with orthogonalized criteria. In Song, Q. C. & Wee. S. (Co-chairs), <em>Multi-Objective Optimization in the Workplace: Addressing Adverse Impact in Selection</em> [Symposium paper]. 35th Annual Convention of the Society for Industrial and Organizational Psychology, Austin, TX.</p>
<p>Song, Q. C., & <strong>Tang, C</strong>. (April 2020). Adverse impact reduction for multiple subgroups: A Pareto-optimization approach. In Song, Q. C. & Wee. S. (Co-chairs), <em>Multi-Objective Optimization in the Workplace: Addressing Adverse Impact in Selection</em> [Symposium paper]. 35th Annual Convention of the Society for Industrial and Organizational Psychology, Austin, TX.</p>
<p><strong>Tang, C.</strong>, Shin, H. J., Barve, A., & Song, Q., C. (April 2020). <em>Using ensemble machine learning to improve assessment in personnel selection</em> [Poster]. 35th Annual Convention of the Society for Industrial and Organizational Psychology, Austin, TX. (Conference canceled)</p>
<p>Sang-Hoon, L., <strong>Tang, C.</strong>, & Liang, Y. J. (April 2020). <em>Won’t stop searching: detachment, self-improvement, and job search outcomes</em> [Poster]. 35th Annual Convention of the Society for Industrial and Organizational Psychology, Austin, TX. (Conference canceled)</p>
<p><strong>Tang, C.</strong>, Chen, Y., Song, Q. C., & Newman, D. A. (April, 2019). <em>Predictor weighting with adverse impact and shrinkage: Reply to Sackett et al. (2017)</em>. Poster presented at the 34th Annual Convention of the Society for Industrial and Organizational Psychology, Washington, DC.</p>
<h2 id="academic-experience">Academic Experience</h2>
<p><strong>School of Labor and Employment Relations, University of Illinois at Urbana–Champaign</strong></p>
<ul>
<li>Research Assistant, 2017-Present</li>
</ul>
<p><strong>School of Entrepreneurship and Management, ShanghaiTech University</strong></p>
<ul>
<li>Research Assistant, 2015-2017</li>
</ul>
<h2 id="teaching-experience">Teaching Experience</h2>
<p>Teaching Assistant, LER 593, School of Labor and Employment Relations, UIUC, Fall 2020</p>
<p>Teaching Assistant, Negotiation, ShanghaiTech SEM, Spring 2016, Spring 2017</p>
<p>Teaching Assistant, Executive MBA Midterm Module, CEIBS, Spring 2017</p></description></item></channel></rss>