langer.soziologie.uni-halle.de · equations appear is arbitrary. the terms used in the level-1...

===============================================================================mla.doc MLA 3.2 05/31/97=============================================================================== Copyright (c) 1993-97 by Frank Busing

Introduction------------

Thank you for your interest in MLA, software for multilevel analysis ofdata with two levels. The main goal of MLA is to provide a program withan easy-to-use interface, alternative estimation methods and extensiveresampling options.

This file contains information about the following topics:

- running MLA - syntax - comments - statements - summary

Running MLA-----------

MLA runs as a stand-alone batch program. It uses an input file and an outputfile as parameters. This means that the program can be started by the command

MLA [-hHv] <inputfile> <outputfile>

where <inputfile> should be replaced by the name of the input file and<outputfile> replaced by the name of the output file. The options arehelp (-h), extended help (-H) and verbosity (-v), respectively.Both input- and output files are simple text files (ASCII).

Syntax------

The input file consists of statements, which are case INsensitive.Every statement begins with a slash and a keyword (e.g., /TITLE).Every keyword may be abbreviated, but it must be at least of length threeto be recognized. Other text following the keyword and/or leading spaceswill be ignored. The rest of the statements must follow on lines below thekeyword and should precede the next statement. These lines are calledsubstatements and may also consist of one or more keywords (e.g., FILE).The last statement to be read is the /END statement. All other statements,and corresponding substatements, may appear in any order (but before the/END statement if they are to be reckoned with). A substatement may continueon the next line. In this case the first line must be ended with twobackslashes (\\).

Comments--------

Comments are preceded by a percent sign (%) and may appear throughoutthe input file. All text on a line, after and including the percent sign,will serve as comment and is ignored as program input.

Statements----------

/TITle (optional)-----------------

Following the keyword /TITle, the first non-blank line contains the titlefor the analysis. The title is repeated on top of every part of the output.

/DATa (required)----------------

The /DATa statement contains information about the data file. This statementhas six substatements, three of which are required.

FILe (required)

This substatement indicates the name of the data file. The name is given after the equals sign and must satisfy the usual DOS conventions on filenames. The file itself is a free-field formatted numbers-only ASCII file. This means that values of variables must be separated by at least one blank. The file must consist of one case per line. Cases must be sorted by the level-2 identifier variable (see below).

VARiables (required)

The VARiables substatement specifies the number of variables in the data file.

ID1 (optional)

One of the variables in the data file MAY contain a code (number) that identifies the level-1 units. The number is used in the output to label level-1 units. The variable number has to follow the keyword ID1 and it must indicate the position of the identifier variable in the data file. The variable number must be at least 1 and less than or equal to the number of variables, indicated on the VARiables substatement. If omitted, the order in which the level-1 units are read from the data file is used as label.

ID2 (required)

One of the variables in the data file MUST contain a code (number) that identifies the level-2 units. The number is essential for a correct discrimination of the level-2 units. Cases must be sorted by the level-2 identifier variable identified on this substatement.

MISsing (optional)

For every variable, one missing value may be specified on this substatement. After the equal sign, first the variable is indicated followed by the missing value between parenthesis. More variables and values are seperated by comma's.

CENTER (optional)

CENTER means Center Grand Mean (Kreft and de Leeuw, 1996). Following the CENTER substatement, the variables must be specified, which will be centered (ingnoring grouping) just after reading the data, but before any analysis. More variables are seperated by comma's.

/MODel (required)-----------------

The /MODel statement is followed by a set of equations that specify the modelthat has to be estimated. There is only one level-1 equation, but there maybe one or more level-2 equations. The order in which the level-1 and level-2

equations appear is arbitrary.The terms used in the level-1 equation are:

- V = variable, which is a variable in the data file. V may be either indicating the outcome variable (V in front of the equal sign) or a predictor variable (V following the equal sign). - B = beta component. At level-1 these are the regression coefficients that seem to be outcome variables at the second level. - E = the level-1 random term. This term is considered to be a residual or error term. The variance of this term has to be estimated from the data.

The level-2 equations partly consist of the same terms, but also of specificlevel-2 equation terms:

- B = beta component, corresponding with the level-1 regression coefficient. At this level, however, B can be viewed as an outcome variable. - G = gamma component. These are the fixed parameters to be estimated in the multilevel model. - V = one of the variables from the data file (as explained above). - U = level-2 random term. As with the first level, this component is considered a residual or error term, but now for the second level. The second level may have more than one error term: one for each level-2 equation (i.e., for each beta element). The variances and the covariances of these terms have to be estimated from the data.

In the equations each term is directly followed by a number (except for thelevel-1 random term E). For the V term this number is the variable number,the position of the variable in the data file (e.g., V4, the fourth variablein the data file). The other terms only use a number for identification,without any additional meaning (e.g., G3, one of the fixed parameters). TheB terms have meaning in the equations of both levels. Every equation consistsof one term before and at least one term after the equals sign. Terms on theright hand side of the equations are connected by plus signs. A variable anda corresponding parameter are connected by an asterisk (*). This is used toconnect a fixed parameter and a predictor variable in level-2 equations and toconnect a level-1 regression coefficient and a predictor variable in thelevel-1 equation.

/CONstraints (optional)-----------------------

The /CONstraints statement allows fixed paramters to be fixed to a certainvalue. Constraints can thus only be applied to fixed parameters and thenof the form: fixed paramter equals certain value, for example G2=2.0. The fixedparamter is held fixed during estimation and is not used for estimation of thestandard errors either. The standard error will be zero and no t-test isperformed for this parameter.

/TEChnical (optional)---------------------

The /TEChnical statement provides useful possibilities to alter theestimation process. If this statement and subsequent substatements are notspecified, the program will run using default values.

ESTimation method (optional)

The substatement ESTimation method provides the opportunity to set the estimation method. One can choose between FIMl and REMl. FIMl is the default method and represents full information maximum likelihood estimation. REMl is restricted maximum likelihood estimation.

MINimization method (optional)

This substatement sets the minimization method. One can choose between BFGS, using the Broyden-Fletcher-Goldfarb-Shanno variant of Davidon-Fletcher-Powell quasi-Newton minimization method, and EM, the Expectation-Maximization method. The default minimization method is BFGS.

REParameterization (optional)

The level-2 covariance matrix should be a positive (semi-)definite matrix. To impose this restrictions, the parameters can be written in the following way: C=LDL', where C is the covariance matrix, L is a lower triangular matrix and D a diagonal matrix. The elements of the diagonal matrix D may either be square ROOTs or powers of e (the complementary of the natural LOGarithm). On default ROOT reparameterization is performed.

WARnings (optional)

If the maximum number of warnings is reached, the program terminates execution. This substatement can change the default value of 25. The value must be an integer between 1 and 32767.

MAXimum number of iterations (optional)

The default value of MAXiter is 100. This number should be sufficient for reaching convergence if the sample size is large enough and/or the number of parameters to be estimated is not too large. Changing the minimization method or the convergence criterion (see below) can make it necessary to raise the maximum number of iterations. The value must be an integer between 1 and 32767.

CONvergence (optional)

After each iteration the new function value is compared to the previous function value. The obtained difference is compared to a convergence related value. If |F[i-1]-F[i]|/{0.5*(|F[i]|+|F[i-1]|)} <= convergence, convergence is said to have been reached. In this formula, F[i] is the function value after the i-th iteration. The default value of CONvergence is 1.0E-08 and permitted values range from 0.0 to 1.0.

SEEd (optional)

For diagnostic purposes, one can provide an initial number (seed) for the random number generator. This is specified by the substatement SEEd. Using the same initial seed, the simulation samples will be identical. The seed value must be an integer between 1 and 1,073,735,823.

LUXury (optional)

Uniform deviates are obtained with te RANLUX pseudo-random number generator (Luscher, 1994). For this generator several types of LUXury may be specified. Five standard levels are defined: 0 = very long period, but fails many tests, 1 = considerable improvement, but still fails some tests, 2 = passes all tests, but theoretically still defective, 3 = default 4 = highest luxury, all 24 bits of mantissa thoroughly chaotic. A higher luxury level also means a slower generation of uniform deviates.

FILe (optional)

Results of the current analysis are written to file. The file must be a valid filename and be specified after the file keyword. Only the essential

information is written to this file. It's content changes over time and some self-inspection will show what is written where.

/SIMulation (optional)----------------------

Several options for simulation are available in MLA. These include jackknife,bootstrap and permutation. Theoretical details concerning the implementationof these resampling methods for the two-level model can be found in the MLAmanual (Busing, Meijer, and van der Leeden, 1994).

KINd (required)

With this substatement the user can choose from three options, namely BOOtstrap, JACkknife and PERmutation simulation. All types of simulation work as follows: 1. perform analysis 2. obtain a (new) sample 3. repeat the analysis 4. save the (new) estimates The last three steps, together called a replication, are repeated a number of times. Afterwards, bias-corrected estimates of model parameters and nonparametric estimates of standard errors are computed. These estimates are computed from the set of saved estimates and the original maximum likelihood estimates.

METhod

This substatement specifies the method of bootstrap to be performed. It is required whenever KINd = BOOtstrap. One can choose between three different methods: 1. RESiduals (or ERRor). This method resamples the elements of the level-1 and level-2 residuals. Subsequently a new outcome or dependent variable is computed using these residuals, the original predictor or independent variables and the parameter estimates (fixed components). 2. CASes. Using this method a bootstrap sample is created by resampling the original data. Thus, complete cases are randomly drawn (with replacement) from the original cases. The procedure follows the nested structure in the data, by a nested resampling of cases: level-2 units are randomly drawn (with replacement) and cases within a particular drawn level-2 unit are drawn (with replacement). 3. PARametric. This method computes a new outcome or dependent variable using the original predictor variables, the parameter estimates and a set of level-1 and level-2 residuals. The residuals are drawn from a normal distribution with mean zero and variance sigma squared for the level-1 residuals, and from a (multivariate) normal distribution with zero mean vector and covariance matrix theta for the level-2 residuals.

TYPe

The substatement type is only required whenever the substatement KINd = BOOtstrap is used in combination with METhod = RESiduals. The TYPe substatement specifies the type of estimation that is used to determine the level-1 and level-2 residuals. One can choose between RAW and SHRunken.

BALancing (optional)

For the bootstrap methods RESiduals and CASes, a balanced bootstrap can be specified on this substatement. In that case BALancing = BALanced must be specified. Default is BALancing = UNBalanced.

RESample (optional)

The substatement RESample offers the user the choice at which level units will be resampled. The default is 0, which means that at both levels units will be resampled. If KINd = JACkknife, or KINd = BOOtstrap and METhod = CASes, the user may choose 1 or 2, which means that only level-1 units or only level-2 units will be resampled, respectively.

LINking

The level-1 and level-2 residuals can be drawn linked or unlinked during simulation. Linking the residuals means that the level-1 residuals will be drawn from the same unit as where the level-2 residual was drawn from. This is specified with LINking = LINked. Specifying LINking = UNLinked has the same result as not using the substatement at all. This is the default.

REPlications (optional)

Using the substatement REPlications the number of bootstrap replications is specified. It must be an integer value between 1 and 32767. The default value is 100.


See the /TEChnical statement. Specifying the CONvergence substatement within the /SIMulation statement has only implications for the convergence during simulation.

FILe (optional)

Results of the simulation analysis can be written to a file. Using the substatement file, a filename may be specified. Filenames must satisfy the usual DOS conventions on filenames.

/INTerval (optional)--------------------

Several options for confidence interval estimation are available in MLA. Theseinclude normal interval, percentile, bias corrected percentile and bootstrap-t.

KINd (required)

With this substatement the user can choose from four methods, namely NORmal, PERcentile, BIAs-corrected percentile and BOOtstrap-t.

WEIght (optional)

This substatement has implications for the internal bootstrap, performed on the bootstrap-t confidence interval estimation. A balanced bootstrap can be specified on this substatement. In that case WEIght = BALanced must be specified. Default is WEIght = UNBalanced.

REPlications (optional)

As for the previous substatement, this substatement has also implications for the bootstrap-t method. The number of internal bootstrap replications is specified. It must be an integer value between 1 and 32767. The default value is 25.

ALPha (optional)

ALPha is the confidence level (two-sided). Now, the confidence interval is

equal to 100(1-2*Alpha). The default value of ALPha is 0.05.


See the /TEChnical statement. Specifying the CONvergence substatement within the /INTerval statement has only implications for the convergence during interval estimation.

FILe (optional)

Results of the interval estimation can be written to a file. Using the substatement file, a filename may be specified. Filenames must satisfy the usual DOS conventions on filenames.

/PRInt (optional)-----------------

The /PRInt statement gives the user control over the output. Not all output isoptional. The default output consists of a title page, an echo of the input,and system information. Output for the simulation analysis is generatedwhenever the /SIMulation statement is used.

INPut

If INPut = YES then the input information is digested and displayed in two parts. A required and an optional part. Default is NO.

DEScriptives

After the keyword descriptives the user may specify both variables and level-2 identification codes. For the total sample size and for every level-2 unit specified the following statistics are computed and displayed: mean, standard deviation, variance, skewness, kurtosis, Kolmogorov- Smirnov's Z, significance level of K-S's Z, minimum, 5th-quantile, first quartile, median, third quartile, 95th quantile and the maximum.

RANdom level-1 coefficients

The random level-1 coefficients or level-2 outcomes consist of ordinary least squares estimates per level-2 unit. After the keyword B's and sigma may be specified.

OLSquares

This part contains the ordinary least squares estimates for the fixed (gamma's) and random (variances and covariances of U and E) parameters. A regression analysis is performed, ignoring grouping. For the level-1 error variance two estimates are displayed, the one-step (E(1)) and two-step (E(2)) estimate.

RESiduals

After the keyword both level-1 and level-2 residuals may be specified (U and E). For the first level, three different types of residuals are displayed, namely the total, raw, and shrunken residuals. The level-2 residuals are the raw and shrunken residuals for the specified level-2 components. These estimates are based on the BFGS-FIML estimates.

POSterior means

Displayed are the posterior means which are specified following the keyword. These estimates are based on the BFGS-FIML estimates.

DIAgnostics

For diagnostic purposes the Mahalanobis distances for the level-2 residuals are displayed.

/PLOt (optional)-----------------

The /PLOt statement gives the user control over some plot options.

HIStograms

This options is only in effect when \SIMULATION is chosen. If so, all parameters may be specified and histograms will be displayed of the specified parameters.

SCAtters

Scatterplots can be obtained for prediction and residuals. Specifying prediction produces a scatterplot of the response variable versus the predicted values based on the estimated fixed parameters. Specifying a variable produces a scatterplot of this variables versus all residuals associated with this variable.

Summary-------

Explanation of the codes used below. <a> means alpha numeric. <filename> means a filename has to be specified. means an integer, possibly followed by the default value. <f> means a floating point, possibly followed by the default value. [a|B] means choose between a and b with B as default. ,... means that more of the same may occur.

/TITLE <a>/DATA file = <filename> variables = id1 = id2 = missing = V(<f>),... center = V,.../MODEL V = E V = B + E (one of these equations) V = B + B*V + ... + E

B = G B = G + G*V + ... B = U ((n)one or more of these equations) B = G + U B = G + G*V + ... + U .../CONSTRAINTS G = <f> .../TECHNICAL estimation method = [FIML|reml] minimization method = [BFGS|em]

reparameterization = [none|ROOT|logarithm] warnings = <i25> maximum number of iterations = <i100> convergence = <f0.00000001> seed = luxury = <i3>/SIMULATION kind = [bootstrap|jackknife|permutation] method = [residuals|cases|parametric] type = [raw|shrunken] resample = [0|1|2] balancing = [UNBALANCED|balanced] linking = [UNLINKED|linked] replications = <i100> convergence = <f0.00000001> file = <filename>/INTERVAL kind = [normal|percentile|bias-corr.|bootstrap-t] replications = <i25> alpha = <f0.10> convergence = <f0.00000001> file = <filename>/PRINT input = [yes|NO] descriptives = V,...,,... random level-1 coefficients = B,...,sigma olsquares = [yes|NO] residuals = U,...,E posterior means = B,... diagnostics = [yes|NO]/PLOT histograms = G,...,U*U,...,E scatters = prediction,V,.../END

An annotated example can be found in MLA.IN.

--- end of mla.doc ------------------------------------------------------------•

Dr. Wolfgang Langer - Methoden V: Grundlagen der Mehrebenenanalyse - WiSe 2000/2001 1

MLA 3.2 Syntaxchart: (MLA.IN)

/TITLE % optional title MLA version 3.2: annotated example

/DATA % specification of data file = mla.dat % data file vars = 6 % total number of variables in data file id1 = 3 % Level-1 identification code variable number id2 = 2 % Level-2 identification code variable number missing = v4(-0.6888) % missing value variable 4 = -0.6888 center = v6 % center grand mean level-1 predictor variable 6

/MODEL % model specification b1 = g1 \\ % lines may be broken + g2*v6 \\ % using two backslashes + u1 % intercept: level-2 equation 1 b2 = g3 + g4*v6 + u2 % slope: level-2 equation 2 v4 = b1 + b2*v5 + e % level-1 equation

/TECHNICAL % additional, technical specifications estimation = fiml % full information maximum likelihood estimation minimization = bfgs % minimization method is dfp:bfgs reparam = root % reparameterization c=ll' warnings = 50 % maximum warnings raised to 50 maximum = 500 % raise maximum number of iterations seed = 1041245 % initial seed to be used luxury = 4 % increase luxury level for random number generator convergence = 1.0E-12 % set convergence criterion

/SIMULATION % specify resample simulation kind = bootstrap % bootstrap simulation analysis method = residuals % resample residuals type = shrunken % use shrunken residuals balance = unbalanced % no balance in resampling linking = unlinked % no linking of level-2 and level-1 residuals replications= 200 % set #replications to 200

/INTERVAL % interval estimation kind = bias-corrected % bias-corrected percentile interval alpha = 0.05 % interval width of 0.90

/PRINT % additional print specification inp = yes % print input specifications des = v4,v5,v6,2,3 % print descriptives of v4,v5,v6, level-2 units 2,3 ols = yes % print ordinary least squares estimates ran = all % print all random level-1 coefficients res = u1,u2 % print residuals u1 and u2 pos = all % print all available posterior means dia = yes % print diagnostics

/PLOT % additional plot specification hist = g2,g3,g4 % plot histograms of g2, g3 and g4 scat = pred,v6,v5 % plot scatterplots: prediction- and residual-plots

/END % final statement: the end.


Beispieldaten für MLA.IN (MLA.DAT)

1 1 1 6.5122 1.7992 0.97481 1 2 -0.6888 -1.4705 0.97481 1 3 -1.0609 -1.6396 0.97481 1 4 1.8257 -0.7967 0.97481 1 5 4.1939 0.3393 0.97481 1 6 0.4208 -1.0766 0.97481 1 7 3.0962 0.2864 0.97481 1 8 8.5943 2.0334 0.97481 1 9 5.7716 0.9920 0.97481 1 10 2.6352 -0.5111 0.97481 1 11 2.2869 0.3637 0.97481 1 12 -0.6532 -1.1865 0.97481 1 13 4.2086 0.5315 0.97481 1 14 2.4606 0.1762 0.97481 1 15 -0.2641 -2.1270 0.97481 1 16 4.3618 1.1520 0.97481 1 17 3.3425 -0.0619 0.97481 1 18 2.4320 -0.6236 0.97481 1 19 2.6399 -0.7329 0.97481 1 20 3.3598 -0.1424 0.97481 2 21 2.4710 -0.6842 0.13281 2 22 3.5291 0.9126 0.13281 2 23 1.8403 1.3195 0.13281 2 24 2.5526 -0.0108 0.13281 2 25 0.6335 -0.1292 0.13281 2 26 2.5231 1.8147 0.13281 2 27 2.2201 -0.9386 0.13281 2 28 1.8413 0.6065 0.13281 2 29 3.0968 -0.8300 0.13281 2 30 1.1467 0.0226 0.13281 2 31 2.7612 -0.8334 0.13281 2 32 -1.3509 -1.9970 0.13281 2 33 -0.1585 -0.2729 0.13281 2 34 1.9577 -1.9295 0.13281 2 35 -0.0129 -0.9837 0.13281 2 36 1.4017 0.8375 0.13281 3 37 -0.5784 -0.0950 -0.44081 3 38 1.0486 0.9250 -0.44081 3 39 2.0903 1.9278 -0.44081 3 40 -0.6303 -1.3346 -0.44081 3 41 0.1564 -0.5883 -0.44081 3 42 -0.0388 -0.4949 -0.44081 3 43 -0.6184 0.2922 -0.44081 3 44 1.9247 0.1411 -0.44081 3 45 3.5335 0.5917 -0.44081 3 46 1.6368 1.8169 -0.44081 3 47 1.3039 0.4692 -0.44081 3 48 0.7818 -0.5333 -0.44081 3 49 1.0610 0.6476 -0.44081 3 50 0.7776 0.1362 -0.44081 3 51 2.5395 0.4815 -0.44081 3 52 0.5413 -0.0836 -0.44081 3 53 2.5396 0.8667 -0.44081 3 54 -0.4255 -1.7238 -0.44081 4 55 2.2620 0.9033 0.72491 4 56 3.5084 -0.5864 0.72491 4 57 1.6510 -0.9267 0.72491 4 58 4.4616 -0.3072 0.72491 4 59 5.7297 0.6002 0.72491 4 60 3.1400 -0.1931 0.72491 4 61 3.6039 0.2698 0.72491 4 62 4.5829 0.4147 0.7249


1 4 63 4.3818 0.4620 0.72491 4 64 3.9561 0.8989 0.72491 4 65 3.9245 -0.8808 0.72491 4 66 4.9539 -0.4200 0.72491 5 67 -0.2942 -1.2687 -0.54351 5 68 0.3290 1.9533 -0.54351 5 69 0.6809 -0.3470 -0.54351 5 70 2.4040 1.8523 -0.54351 5 71 -0.2593 0.2563 -0.54351 5 72 1.6647 0.9387 -0.54351 5 73 -1.1033 0.2525 -0.54351 5 74 1.5945 0.7525 -0.54351 5 75 0.3558 0.3228 -0.54351 5 76 3.4318 1.6264 -0.54351 5 77 0.8004 0.3197 -0.54351 5 78 -2.2108 -1.0837 -0.54351 5 79 2.3819 1.6530 -0.54351 5 80 -0.3729 -0.7450 -0.54351 5 81 -1.0694 -0.6574 -0.54351 6 82 -0.1857 0.0278 -0.80771 6 83 -0.7354 0.7777 -0.80771 6 84 0.9252 -0.0477 -0.80771 6 85 -0.1627 -0.6685 -0.80771 6 86 -3.5414 0.7633 -0.80771 6 87 0.1727 0.7812 -0.80771 6 88 -0.7255 -0.1700 -0.80771 6 89 -1.7471 1.0326 -0.80771 6 90 1.1392 1.0010 -0.80771 6 91 0.6142 2.3420 -0.80771 6 92 0.8258 -1.3006 -0.80771 6 93 -0.4871 0.3019 -0.80771 6 94 -0.2660 1.7809 -0.80771 6 95 -0.6936 0.3123 -0.80771 6 96 0.3327 -0.9033 -0.80771 7 97 -2.1265 -0.8029 0.29001 7 98 -0.0065 -2.0474 0.29001 7 99 0.2993 -0.4022 0.29001 7 100 -0.1612 -2.3101 0.29001 7 101 -0.8787 -1.2936 0.29001 7 102 -1.1090 -1.1250 0.29001 7 103 0.2497 -0.6848 0.29001 7 104 1.9083 1.1305 0.29001 7 105 -0.3828 0.7619 0.29001 7 106 -0.7460 -0.7279 0.29001 7 107 0.9295 1.5908 0.29001 7 108 -0.6341 -0.5583 0.29001 7 109 -1.6709 -0.4074 0.29001 8 110 -0.1568 -0.6910 0.33471 8 111 0.9903 -0.8203 0.33471 8 112 2.3904 1.6722 0.33471 8 113 1.6646 -0.8886 0.33471 8 114 1.2441 0.5597 0.33471 8 115 3.0712 0.7239 0.33471 8 116 -0.6587 -1.1808 0.33471 8 117 -0.1398 -1.2458 0.33471 8 118 3.3909 0.4897 0.33471 8 119 2.1414 0.3809 0.33471 8 120 0.5790 -0.1332 0.33471 8 121 1.6215 0.6711 0.33471 8 122 -2.1556 -1.3341 0.33471 9 123 -2.9402 0.9547 -1.43651 9 124 -0.8171 0.7389 -1.43651 9 125 -1.4535 -1.1067 -1.43651 9 126 -1.6405 -0.8912 -1.43651 9 127 -1.6881 -0.6136 -1.43651 9 128 -0.4534 0.6689 -1.4365


1 9 129 -3.0075 -0.7839 -1.43651 9 130 -2.4737 0.0537 -1.43651 9 131 -1.9475 0.7113 -1.43651 9 132 -1.1980 1.6367 -1.43651 9 133 -1.1151 1.5539 -1.43651 9 134 -2.7974 2.1273 -1.43651 9 135 -2.2646 0.5495 -1.43651 9 136 -1.8518 0.5363 -1.43651 9 137 -0.9556 0.0848 -1.43651 10 138 2.5111 0.4500 0.07921 10 139 0.0585 -0.0209 0.07921 10 140 -0.1860 -0.2794 0.07921 10 141 0.3206 0.1063 0.07921 10 142 1.2966 0.2026 0.07921 10 143 -0.8540 -0.7788 0.07921 10 144 0.2108 0.4217 0.07921 10 145 -0.4629 -0.7956 0.07921 10 146 -0.7029 -0.9923 0.07921 10 147 2.1545 1.1346 0.07921 10 148 0.6504 0.1678 0.07921 10 149 -0.3809 -0.0634 0.07921 10 150 2.9531 0.5709 0.07921 10 151 0.8051 0.9562 0.07921 11 152 -1.2992 1.0344 -0.23261 11 153 -0.8327 0.2478 -0.23261 11 154 -0.1879 1.2143 -0.23261 11 155 -1.2143 -0.6602 -0.23261 11 156 -2.9049 -1.4581 -0.23261 11 157 0.0537 0.4856 -0.23261 11 158 -0.8992 -1.5424 -0.23261 11 159 -1.9036 -0.5016 -0.23261 11 160 1.4093 -0.3951 -0.23261 11 161 -1.2953 0.6563 -0.23261 11 162 -0.1940 0.7158 -0.23261 11 163 0.9516 0.1920 -0.23261 11 164 -3.3130 -1.4106 -0.23261 11 165 -1.2113 -1.1319 -0.23261 11 166 -1.0919 -0.9798 -0.23261 11 167 1.6425 1.3930 -0.23261 11 168 -2.4071 -2.2189 -0.23261 11 169 -2.4593 -1.4673 -0.23261 11 170 -0.2639 -0.2951 -0.23261 12 171 2.6092 0.7390 0.24821 12 172 2.2086 0.0302 0.24821 12 173 1.0234 -0.6033 0.24821 12 174 4.2309 1.1759 0.24821 12 175 1.1114 0.6201 0.24821 12 176 -0.1447 -1.0779 0.24821 12 177 0.1832 -0.2484 0.24821 12 178 1.6998 0.1584 0.24821 12 179 6.2600 2.5213 0.24821 12 180 6.5219 1.4943 0.24821 12 181 5.9366 2.0416 0.24821 12 182 3.4965 1.1490 0.24821 12 183 0.5094 -1.0199 0.24821 12 184 3.9805 0.9869 0.24821 12 185 0.4391 -1.5306 0.24821 12 186 3.0649 0.4854 0.24821 13 187 -0.7234 -1.2928 -0.28111 13 188 0.3593 0.6443 -0.28111 13 189 0.7426 0.3177 -0.28111 13 190 2.4067 2.1622 -0.28111 13 191 -0.4378 1.4028 -0.28111 13 192 2.0761 -0.4092 -0.28111 13 193 -0.8861 -0.5151 -0.28111 13 194 2.3963 0.8219 -0.2811


1 13 195 0.6361 -1.7016 -0.28111 13 196 2.9052 2.5676 -0.28111 13 197 -1.7792 -0.0301 -0.28111 13 198 0.6447 -1.6370 -0.28111 13 199 -1.8512 -0.5599 -0.28111 13 200 0.2123 -0.3008 -0.28111 14 201 -1.0915 -0.9518 -0.15321 14 202 1.2340 0.2044 -0.15321 14 203 0.7601 -0.9350 -0.15321 14 204 1.2566 -0.0983 -0.15321 14 205 -0.5684 0.9301 -0.15321 14 206 3.6032 1.8211 -0.15321 14 207 2.6902 1.7191 -0.15321 14 208 0.4270 0.6793 -0.15321 14 209 0.1306 0.7735 -0.15321 14 210 3.0406 1.0295 -0.15321 14 211 0.5976 0.0473 -0.15321 14 212 2.3063 0.7182 -0.15321 14 213 1.2056 -0.2637 -0.15321 14 214 0.9445 -1.3279 -0.15321 14 215 0.5704 0.7842 -0.15321 14 216 1.6062 0.7338 -0.15321 14 217 0.2291 -0.9384 -0.15321 15 218 4.6728 1.0152 0.16691 15 219 0.7644 -0.0356 0.16691 15 220 3.1868 -0.0749 0.16691 15 221 2.5073 0.5224 0.16691 15 222 0.4301 -0.9969 0.16691 15 223 1.7342 -0.5023 0.16691 15 224 -1.7790 -1.2205 0.16691 15 225 2.1434 0.2852 0.16691 15 226 1.0484 -0.3720 0.16691 15 227 3.1646 -0.0047 0.16691 15 228 5.3879 1.6764 0.16691 15 229 1.4748 -0.1866 0.16691 15 230 3.5825 0.3128 0.16691 15 231 4.0295 0.2066 0.1669


Ausgabeprotokoll von MLA32 (MLA.OUT):

MMMM MMMMM LLLL AAAAAAAA MMMMM MMMMMM LLLL AAAAAAAAAA MMMM M MMMMMMM LLLL AAAA AAAA MMMM MM MMM MMMM LLLL AAAA AAAA MMMM MMMM MMMM LLLL AAAA AAAA MMMM MM MMMM LLLL AAAAAAAAAAAAAAAAAA MMMM M MMMM LLLL AAAAAAAAAAAAAAAAAAAA MMMM MMMM LLLL AAAA AAAA MMMM MMMM LLLL AAAA AAAA MMMM MMMM LLLL AAAA MMMM MMMM LLLLLLLLLLLLLLLLLLLLLLLLLLLL AAAA MMMM MMMM LLLLLLLLLLLLLLLLLLLLLLLLLLLLLL AAAA AAAA Multilevel Analysis for Two Level Data AAAA AAAA Version 3.2 AAAA AAAA Developed by AAAA Frank Busing AAAA Erik Meijer AAAA Rien van der Leeden AAAA AAAA Published by AAAA Leiden University AAAA Faculty of Social and Behavioural Sciences AAAA Department of Psychometrics and Research Methodology AAAA Wassenaarseweg 52 AAAA P.O. Box 9555 AAAA 2300 RB Leiden AAAA The Netherlands AAAA Phone +31 (0)71-273761 AAAA Fax +31 (0)71-273619 AAAA


MLA (R) Multilevel Analysis for Two Level Data Version 3.2 05-31-1997 Copyright 1993-1997 Leiden University All Rights Reserved Part 1

Wed Oct 11 14:07:18 2000

Inputfile statements

1 /TITLE % optional title 2 MLA version 3.2: annotated example 3 /DATA % specification of data 4 file = mla.dat % data file 5 vars = 6 % total number of variables in data file 6 id1 = 3 % Level-1 identification code variable number 7 id2 = 2 % Level-2 identification code variable number 8 missing = v4(-0.6888) % missing value variable 4 = -0.6888 9 center = v6 % center grand mean level-1 predictor variable 6 10 /MODEL % model specification 11 b1 = g1 \\ % lines may be broken 12 + g2*v6 \\ % using two backslashes 13 + u1 % intercept: level-2 equation 1 14 b2 = g3 + g4*v6 + u2 % slope: level-2 equation 2 15 v4 = b1 + b2*v5 + e % level-1 equation 16 /TECHNICAL % additional, technical specifications 17 estimation = fiml % full information maximum likelihood estimation 18 minimization = bfgs % minimization method is dfp:bfgs 19 reparam = root % reparameterization c=ll' 20 warnings = 50 % maximum warnings raised to 50 21 maximum = 500 % raise maximum number of iterations 22 seed = 1041245 % initial seed to be used 23 luxury = 4 % increase luxury level for random number generator 24 convergence = 1.0E-12 % set convergence criterion 25 /SIMULATION % specify resample simulation 26 kind = bootstrap % bootstrap simulation analysis 27 method = residuals % resample residuals 28 type = shrunken % use shrunken residuals 29 balance = unbalanced % no balance in resampling 30 linking = unlinked % no linking of level-2 and level-1 residuals 31 replications= 200 % set #replications to 200 32 /INTERVAL % interval estimation 33 kind = bias-corrected % bias-corrected percentile interval 34 alpha = 0.05 % interval width of 0.90 35 /PRINT % additional print specification 36 inp = yes % print input specifications 37 des = v4,v5,v6,2,3 % print descriptives of v4,v5,v6, level-2 units 2,3 38 ols = yes % print ordinary least squares estimates 39 ran = all % print all random level-1 coefficients 40 res = u1,u2 % print residuals u1 and u2 41 pos = all % print all available posterior means 42 dia = yes % print diagnostics 43 /PLOT % additional plot specification 44 hist = g2,g3,g4 % plot histograms of g2, g3 and g4 45 scat = pred,v6,v5 % plot scatterplots: prediction- and residual-plots 46 /END % final statement: the end.

46 lines read from "mla.in"



Wed Oct 11 14:07:18 2000 MLA version 3.2: annotated example

Input information

Required

Name of datafile : MLA.DAT Number of variables : 6 Level-2 id. column : 2 Equation 1 : B1=G1+G2*V6+U1 Equation 2 : B2=G3+G4*V6+U2 Equation 3 : V4=B1+B2*V5+E Single equation : V4=E0+G1+G2*V6+G3*V5+G4*V6*V5+U1+U2*V5

Optional

Title of analysis : MLA version 3.2: annotated example Level-1 id. column : 3 Missing for var 4 : -0.688800 Center variables : V6 Estimation method : 1 Minimization method : 1 Reparameterization : 1 Maximum iterations : 500 Convergence : 1e-12 Warnings (maximum) : 50 Kind of simulation : 1 Simulation method : 3 Simulation balance : 0 Simulation linking : 0 Residuals type : 2 Resampling type : 0 Luxury level : 4 Initial random seed : 1041245 Simulation convergence : 1e-10 Number of replications : 200 Simulation output file : Kind of CI estimation : 0.000000 CI alpha : 0.050000 CI convergence : 1e-10 CI replications : 25 Print input : 1 Print explore : 1, V4,V5,V6,2,3 Print olsq : 1 Print outcomes : ALL Compute residuals : 1 Print residuals : U1,U2 Print posterior means : ALL Print diagnostics : 1 Print intervals : 1 Max equations : 3 Level-1 size : 2 Level-2 : 2 X-size : 4 Z-size : 2 Parameters : 8 Level-2 parameters : 3 Input file : mla.in Output file : mla.out Verbose : 0 Monte Carlo : 0


Monte Carlo file : Plot histograms : G2,G3,G4 Plot scatterplots : PRED,V6,V5 Response variable : 4 Explanatory variables : 0(1) 6(2) 5(3) 6(4) Random level-2 vars. : 0(1) 5(2) Random level-1 coeffs. : 0(1) 5(2) Level-2 outcome 1 : 0(1)[1] 6(2)[1] Level-2 outcome 2 : 0(3)[2] 6(4)[2]



Data descriptives

Data descriptives for all units # Level-1 units = 231 # missing Level-1 units = 1 # correct Level-1 units = 230 # correct Level-2 units = 15

Var Mean Stddev Variance Skewness Kurtosis K-S Z Prob(Z)

4 0.98 2.08 4.34 0.50 0.26 0.91 0.38 5 0.07 1.01 1.03 0.06 -0.48 0.68 0.75 6 0.00 0.59 0.34 -0.37 0.17 1.68 0.00

Var Minimum P5 Q1 Median Q3 P95 Maximum

4 -3.54 8.59 8.59 8.59 8.59 8.59 8.59 5 -2.31 2.57 2.57 2.57 2.57 2.57 2.57 6 -1.37 1.04 1.04 1.04 1.04 1.04 1.04

Data descriptives for level-2 unit 2 # Level-1 units = 16


4 1.65 1.32 1.73 -0.71 -0.48 0.73 0.66 5 -0.19 1.09 1.19 0.09 -1.00 0.47 0.98 6 0.20 0.00 0.00 -0.91 -2.12 3.37 0.00


4 -1.35 3.53 3.53 3.53 3.53 3.53 3.53 5 -2.00 1.81 1.81 1.81 1.81 1.81 1.81 6 0.20 0.20 0.20 0.20 0.20 0.20 0.20

Data descriptives for level-2 unit 3 # Level-1 units = 18


4 0.98 1.23 1.51 0.31 -1.00 0.44 0.99 5 0.19 0.94 0.88 -0.09 -0.39 0.42 0.99 6 -0.37 0.00 0.00 0.92 -2.11 3.57 0.00



4 -0.63 3.53 3.53 3.53 3.53 3.53 3.53 5 -1.72 1.93 1.93 1.93 1.93 1.93 1.93 6 -0.37 -0.37 -0.37 -0.37 -0.37 -0.37 -0.37



Random Level-1 coefficients: ordinary least squares estimates per level-2 unit

Parameter B1

Unit Size Estimate SE T Prob(T)

1 19 3.0888 0.2037 15.16 0.0000 2 16 1.7388 0.3223 5.40 0.0000 3 18 0.8177 0.2317 3.53 0.0004 4 12 3.8383 0.3320 11.56 0.0000 5 15 0.1274 0.2790 0.46 0.6481 6 15 -0.2244 0.3394 -0.66 0.5085 7 13 -0.1003 0.3034 -0.33 0.7409 8 13 1.2527 0.2887 4.34 0.0000 9 15 -1.7832 0.2339 -7.62 0.0000 10 14 0.4844 0.2179 2.22 0.0261 11 19 -0.6488 0.2568 -2.53 0.0115 12 16 1.9309 0.2503 7.72 0.0000 13 14 0.4166 0.3705 1.12 0.2608 14 17 0.8941 0.2680 3.34 0.0008 15 14 2.2108 0.2497 8.85 0.0000

Mean 0.9363 Variance 2.1348

Parameter B2


1 19 2.0601 0.1895 10.87 0.0000 2 16 0.4419 0.3002 1.47 0.1410 3 18 0.8495 0.2488 3.41 0.0006 4 12 0.4088 0.5288 0.77 0.4395 5 15 1.1025 0.2526 4.36 0.0000 6 15 -0.1937 0.3318 -0.58 0.5593 7 13 0.4398 0.2501 1.76 0.0786 8 13 1.2821 0.3117 4.11 0.0000 9 15 0.0231 0.2291 0.10 0.9197 10 14 1.4745 0.3542 4.16 0.0000 11 19 0.8319 0.2360 3.53 0.0004 12 16 1.7677 0.2106 8.39 0.0000 13 14 0.5910 0.2922 2.02 0.0431 14 17 0.7598 0.2809 2.70 0.0068 15 14 2.2331 0.3470 6.44 0.0000



Parameter SIGMA


1 19 0.7855 0.2694 2.92 0.0035 2 16 1.6077 0.6077 2.65 0.0081 3 18 0.9254 0.3272 2.83 0.0046 4 12 1.3212 0.5908 2.24 0.0253 5 15 1.0233 0.4014 2.55 0.0107 6 15 1.4612 0.5731 2.55 0.0107 7 13 0.9695 0.4134 2.35 0.0190 8 13 1.0595 0.4518 2.35 0.0190 9 15 0.6855 0.2689 2.55 0.0107 10 14 0.6540 0.2670 2.45 0.0143 11 19 1.1433 0.3921 2.92 0.0035 12 16 0.8693 0.3286 2.65 0.0081 13 14 1.9089 0.7793 2.45 0.0143 14 17 1.1083 0.4047 2.74 0.0061 15 14 0.8698 0.3551 2.45 0.0143


Note: random level-1 coefficients are also referred to as level-2 outcomes See documentation for further elaboration on this subject



Ordinary least squares estimates

Fixed parameters

Label Estimate SE

G1 0.964629 0.086684 G2 2.090289 0.150299 G3 1.056595 0.085498 G4 0.793350 0.148707

Random parameters

Label Estimate SE

E(1) 1.683346 0.158356

U1*U1 0.579149 0.211475 U2*U1 0.034622 0.115429 U2*U2 0.343020 0.125253

E(2) 0.942747 0.088686

E(1): one-step estimate of sigma squared (ignoring grouping) E(2): two-step estimate of sigma squared See documentation for further elaboration on these subjects




Full information maximum likelihood estimates (BFGS)

Fixed parameters

Label Estimate SE T Prob(T)

G1 0.936989 0.190592 4.92 0.0000 G2 2.058120 0.327704 6.28 0.0000 G3 0.956199 0.127996 7.47 0.0000 G4 0.737448 0.219790 3.36 0.0007

Random parameters

Label Estimate SE T Prob(T)

U1*U1 0.467356 0.198821 2.35 0.0187 U2*U1 0.050104 0.094816 0.53 0.5972 U2*U2 0.160850 0.088703 1.81 0.0697

E 1.096541 0.109506 10.01 0.0000

Conditional intra-class correlation = 0.47/(1.10+0.47) = 0.2988

# iterations = 10 -2*Log(L) = 720.520970



Residuals

Level-2 residuals U1

Unit Raw Shrunken

1 0.0039 0.0077 2 0.3869 0.3482 3 0.6464 0.5787 4 1.2678 1.0222 5 0.1673 0.2066 6 0.3593 0.2123 7 -1.7758 -1.4021 8 -0.5147 -0.4359 9 0.0947 0.0908 10 -0.7572 -0.6209 11 -1.2487 -1.1068 12 0.3415 0.3649 13 -0.0834 -0.0827 14 0.1308 0.0979 15 0.7887 0.7189

Mean -0.0128 -0.4533 Variance 0.6180 1.3033 Covariance 0.0000 0.0611


K-S Z 0.7603 0.5352 Prob(Z) 0.6099 0.9369

Level-2 residuals U2

Unit Raw Shrunken

1 0.3343 0.2534 2 -0.6630 -0.4739 3 0.1676 0.1450 4 -1.1327 -0.3842 5 0.4963 0.3554 6 -0.6050 -0.3715 7 -0.7810 -0.5131 8 0.0283 0.0070 9 0.0755 0.0561 10 0.4092 0.1255 11 -0.0035 -0.0016 12 0.5778 0.4442 13 -0.2087 -0.1610 14 -0.1342 -0.0817 15 1.1031 0.6003

Mean -0.0224 -0.0834 Variance 0.3474 0.8108 Covariance -0.0000 0.0028 K-S Z 0.4398 0.6708 Prob(Z) 0.9903 0.7591

Note: shrunken level-2 residuals are also referred to as conditional means Note: covariance refers to covariance with corresponding level-1 residuals See documentation for further elaboration on this subject



Posterior means

Parameter B1

Unit Estimate

1 3.0926 2 1.7002 3 0.7501 4 3.5927 5 0.1666 6 -0.3714 7 0.2733 8 1.3316 9 -1.7870 10 0.6207 11 -0.5069 12 1.9543 13 0.4173 14 0.8613 15 2.1411



Parameter B2

Unit Estimate

1 1.9792 2 0.6310 3 0.8269 4 1.1574 5 0.9616 6 0.0398 7 0.7077 8 1.2608 9 0.0037 10 1.1909 11 0.8338 12 1.6342 13 0.6386 14 0.8122 15 1.7303


Note: posterior means = shrunken estimates of random level-1 coefficients See documentation for further elaboration on this subject



Diagnostics

Level-2 sample size = 15 Total sample size = 230 Mean Level-1 sample size = 15 Effective sample size = 44

Squared correlation coefficients

Norm based R-squared = 0.627456 Grand mean based R-squared = 0.614517 Context mean based R-squared = 0.240201 Trimmed mean based R-squared = 0.485713

Level-1 outliers (sorted by Prob)

Level-1 Level-2 Level-1 Unit Unit Unit T Prob

86 6 5 -0.013931 0.988885 160 11 9 0.010492 0.991629 45 3 9 0.009728 0.992238 32 2 12 -0.009702 0.992258 197 13 11 -0.009574 0.992361 205 14 5 -0.009535 0.992392 68 5 2 -0.008580 0.993154 180 12 10 0.008569 0.993162 55 4 1 -0.008552 0.993176 199 13 13 -0.008514 0.993206 175 12 5 -0.008421 0.993281 192 13 6 0.008357 0.993331 57 4 3 -0.007949 0.993657


33 2 13 -0.007810 0.993768 29 2 9 0.007581 0.993951 122 8 13 -0.007463 0.994045 43 3 7 -0.007404 0.994092 191 13 5 -0.007400 0.994095 97 7 1 -0.007354 0.994132 59 4 5 0.007235 0.994227 150 10 13 0.007151 0.994294 90 6 9 0.006846 0.994537 113 8 4 0.006818 0.994559 11 1 10 -0.006818 0.994560 104 7 8 0.006644 0.994699 76 5 10 0.006643 0.994699 152 11 1 -0.006641 0.994701 118 8 9 0.006639 0.994703 73 5 7 -0.006633 0.994707 194 13 8 0.006567 0.994760 164 11 13 -0.006553 0.994771 163 11 12 0.006333 0.994947 109 7 13 -0.006116 0.995120 31 2 11 0.006113 0.995122 22 2 2 0.006097 0.995135 219 15 2 -0.006008 0.995206 210 14 10 0.005997 0.995215 138 10 1 0.005992 0.995219 231 15 14 0.005966 0.995239 209 14 9 -0.005939 0.995261 206 14 6 0.005826 0.995351 89 6 8 -0.005814 0.995361 35 2 15 -0.005789 0.995381 8 1 7 0.005787 0.995382 37 3 1 -0.005782 0.995386 128 9 6 0.005777 0.995390 51 3 15 0.005770 0.995396 177 12 7 -0.005752 0.995410 12 1 11 -0.005704 0.995449 91 6 10 0.005681 0.995467 66 4 12 0.005658 0.995485 224 15 7 -0.005557 0.995566 201 14 1 -0.005549 0.995572 195 13 9 0.005385 0.995703 185 12 15 0.005336 0.995742 129 9 7 -0.005302 0.995769 198 13 12 0.005255 0.995807 161 11 10 -0.005241 0.995818 123 9 1 -0.005183 0.995864 78 5 12 -0.005026 0.995990 220 15 3 0.005025 0.995990 84 6 3 0.005013 0.996000 167 11 16 0.004978 0.996028 16 1 15 -0.004836 0.996141 151 10 14 -0.004788 0.996179 34 2 14 0.004710 0.996242 134 9 12 -0.004674 0.996270 19 1 18 0.004663 0.996279 214 14 14 0.004656 0.996285 25 2 5 -0.004607 0.996323 156 11 5 -0.004585 0.996341 21 2 1 0.004547 0.996371 158 11 7 0.004539 0.996378 15 1 14 0.004523 0.996391 112 8 3 -0.004423 0.996471 193 13 7 -0.004388 0.996498 98 7 2 0.004371 0.996512 14 1 13 -0.004357 0.996524 44 3 8 0.004339 0.996538


53 3 17 0.004332 0.996543 208 14 8 -0.004322 0.996551 67 5 1 0.004295 0.996573 196 13 10 0.004269 0.996594 227 15 10 0.004238 0.996618 100 7 4 0.004198 0.996650 124 9 2 0.004171 0.996671 69 5 3 0.004115 0.996717 215 14 15 -0.004042 0.996775 27 2 7 0.003938 0.996857 144 10 7 -0.003936 0.996859 115 8 6 0.003913 0.996877 221 15 4 -0.003825 0.996948 212 14 12 0.003809 0.996961 159 11 8 -0.003681 0.997063 137 9 15 0.003629 0.997104 24 2 4 0.003598 0.997129 92 6 11 0.003509 0.997200 111 8 2 0.003469 0.997232 3 1 2 -0.003393 0.997293 149 10 12 -0.003392 0.997293 58 4 4 0.003291 0.997373 114 8 5 -0.003192 0.997453 46 3 10 -0.003184 0.997459 190 13 4 0.003130 0.997502 36 2 16 -0.003108 0.997520 225 15 8 -0.003096 0.997530 130 9 8 -0.003040 0.997574 230 15 13 0.002959 0.997639 71 5 5 -0.002941 0.997653 103 7 7 0.002862 0.997716 223 15 6 0.002835 0.997737 9 1 8 0.002809 0.997758 74 5 8 0.002802 0.997764 133 9 11 0.002779 0.997783 170 11 19 0.002771 0.997789 171 12 1 -0.002760 0.997797 18 1 17 0.002760 0.997798 60 4 6 -0.002722 0.997828 105 7 9 -0.002714 0.997834 30 2 10 -0.002646 0.997888 10 1 9 0.002634 0.997898 169 11 18 -0.002592 0.997931 7 1 6 -0.002560 0.997957 99 7 3 0.002534 0.997978 203 14 3 0.002533 0.997978 62 4 8 0.002527 0.997983 228 15 11 -0.002490 0.998013 20 1 19 0.002481 0.998020 38 3 2 -0.002439 0.998054 154 11 3 -0.002414 0.998074 87 6 6 0.002411 0.998076 132 9 10 0.002406 0.998080 88 6 7 -0.002347 0.998127 110 8 1 -0.002301 0.998164 102 7 6 -0.002258 0.998198 142 10 5 0.002257 0.998199 213 14 13 0.002249 0.998205 178 12 8 -0.002246 0.998207 120 8 11 -0.002210 0.998236 72 5 6 0.002208 0.998238 135 9 13 -0.002172 0.998267 121 8 12 -0.002161 0.998276 207 14 7 0.002153 0.998281 23 2 3 -0.002117 0.998311 81 5 15 -0.002074 0.998345


182 12 12 -0.002046 0.998367 6 1 5 -0.001978 0.998421 65 4 11 0.001961 0.998435 222 15 5 0.001958 0.998438 188 13 2 -0.001925 0.998463 204 14 4 0.001921 0.998467 42 3 6 -0.001917 0.998470 79 5 13 0.001899 0.998484 48 3 12 0.001833 0.998537 95 6 14 -0.001796 0.998567 5 1 4 0.001785 0.998576 119 8 10 0.001759 0.998596 116 8 7 -0.001747 0.998606 181 12 11 0.001743 0.998609 139 10 2 -0.001736 0.998614 153 11 2 -0.001714 0.998632 96 6 15 0.001679 0.998660 183 12 13 0.001676 0.998662 17 1 16 0.001675 0.998663 165 11 14 0.001666 0.998670 4 1 3 0.001662 0.998673 187 13 1 -0.001652 0.998681 166 11 15 0.001635 0.998695 39 3 3 -0.001604 0.998720 83 6 2 -0.001583 0.998736 125 9 3 0.001561 0.998754 63 4 9 0.001558 0.998756 61 4 7 -0.001515 0.998791 211 14 11 -0.001461 0.998834 226 15 9 -0.001458 0.998837 107 7 11 0.001451 0.998842 106 7 10 -0.001430 0.998858 80 5 14 0.001411 0.998874 77 5 11 0.001409 0.998876 141 10 4 -0.001409 0.998876 229 15 12 -0.001403 0.998880 40 3 4 -0.001381 0.998897 49 3 13 -0.001348 0.998924 184 12 14 0.001340 0.998930 94 6 13 0.001333 0.998936 157 11 6 0.001312 0.998953 108 7 12 -0.001266 0.998989 1 1 1 -0.001244 0.999007 186 12 16 0.001213 0.999032 146 10 9 0.001212 0.999032 140 10 3 -0.001136 0.999094 64 4 10 -0.001097 0.999124 70 5 4 0.001030 0.999177 145 10 8 0.000992 0.999208 172 12 2 0.000986 0.999213 174 12 4 0.000972 0.999224 54 3 18 0.000971 0.999225 101 7 5 -0.000920 0.999266 52 3 16 -0.000903 0.999279 117 8 8 0.000899 0.999282 93 6 12 -0.000897 0.999284 218 15 1 0.000856 0.999316 143 10 6 -0.000835 0.999333 202 14 2 0.000811 0.999353 131 9 9 -0.000794 0.999366 176 12 6 -0.000747 0.999403 28 2 8 -0.000727 0.999419 126 9 4 0.000717 0.999427 41 3 5 -0.000710 0.999433 173 12 3 0.000698 0.999442 50 3 14 -0.000685 0.999453


216 14 16 0.000679 0.999458 162 11 11 -0.000618 0.999507 189 13 3 0.000607 0.999515 179 12 9 -0.000562 0.999551 75 5 9 -0.000560 0.999553 127 9 5 0.000480 0.999617 56 4 2 -0.000396 0.999684 47 3 11 0.000385 0.999693 168 11 17 0.000384 0.999693 148 10 11 -0.000358 0.999714 136 9 14 -0.000356 0.999716 85 6 4 -0.000297 0.999762 217 14 17 0.000210 0.999832 82 6 1 0.000193 0.999845 200 13 14 -0.000116 0.999907 13 1 12 0.000109 0.999913 26 2 6 -0.000077 0.999938 155 11 4 -0.000071 0.999943 147 10 10 -0.000012 0.999990

Level-2 Mahalanobis distances (sorted by Prob(M))

Unit M Prob(M)

7 5.052856 0.080910 4 3.803597 0.149863 15 2.866619 0.238823 11 2.709150 0.258324 2 1.940617 0.379085 12 1.340144 0.511717 6 1.095992 0.578134 10 1.062185 0.587987 5 0.805649 0.668441 3 0.760907 0.683561 8 0.425112 0.808517 1 0.410341 0.814510 13 0.163562 0.921474 14 0.075243 0.963077 9 0.031497 0.984375

Effective sample size: N/(1+(N/J-1)*intra-class correlation) Squared correlation coefficients (R-squared) are highly speculative in nature Prob(M): probability - area under the curve of the chi-square distribution See documentation for further elaboration on this subject



Bootstrap estimates (unbalanced unlinked shrunken residuals)

Replications done = 200 Replications used = 200


Fixed parameters

Label Estimate SE

G1 0.944797 0.179150 G2 2.068535 0.285512 G3 0.961233 0.108261 G4 0.731055 0.182280

Random parameters

Label Estimate SE

U1*U1 0.578065 0.172118 U2*U1 0.042871 0.088992 U2*U2 0.226534 0.056834

E 1.199863 0.089640



Confidence interval estimates (bias-corrected percentile method)

Fixed parameters

Label Estimate Mean Lower Upper

G1 0.936989 0.929181 0.653897 1.264194 G2 2.058120 2.047704 1.661298 2.604263 G3 0.956199 0.951164 0.827148 1.185824 G4 0.737448 0.743840 0.386996 1.032780

Random parameters

Label Estimate Mean Lower Upper

U1*U1 0.467356 0.356646 0.268164 0.912968 U2*U1 0.050104 0.057337 -0.076812 0.230282 U2*U2 0.160850 0.095165 0.135073 0.248142

E 1.096541 0.993219 1.026286 1.231799

Note: mean refers to average over bootstrap replications See documentation for further elaboration on this subject




Scatterplots

6.5941 +----------------+------------------------------------------+ | | | 1 1| | | | | | 1 1 | p | 1 | r | 1 1 1 1 | e | 1 11 1 1 1 | d | 1 2 1 21 1 1 | i | 1 11 1121 1 1 | c | 1 21 213 2 21 1 | t | 1 13 231 2 11 1 1 | e | 1 1 2213432 122 11 1 2 1 | d | 1 13 3131151 11 31 1 | | 1 1 112111 12 1223 11111 1 | | 113 4211231213 1 2 | +11 1 1 3 312*2 122 + | 1 1 12112 111 1 | | 1 1 1 | | 21 11122 2111 | -1.9893 +----------------+------------------------------------------+ -3.5414 observed 8.5943

Scatterplot predicted vs observed

2.2941 +---------------------------+-------------------------------+ | 1 | | 1 1 | | 1 2 | | 1 11 1 12 1 1 1 1 | |1 1 11 11 1 1 1 2 1 11 1 11 1 | | 1 2 1 1 2 1 1 21 1 1 1| r | 1 21 2 1 1 2 121 111 1 1 | e | 1 1 1 311112 1 311 1 1 1 2 1 | s + 1 1 132 112 1 * 1 113 1 1 1 1 + i | 1 11 1 111 11 1212 113 1 1 | d | 113 2 11 113 21131 1122 1 1 1 1 | u | 1 1 2 1 1 1 11 1 1 1 | a | 1 1 2 11 1 1 11 2 1 1 1 | l | 1 11 1 1 1 11 12 1 | | 1 1 1 21 1 1 1 | | 1 11 1 1 1 | | 1 1 | | 1 | | | | 1 | -3.2004 +---------------------------+-------------------------------+ -2.3101 predictor 2.5676

Scatterplot predictor V5 vs residual E




Scatterplots (resumed)

1.0222 +---------------------------------+-------------------------+ | 1 | | | | | | 1 | | 1 | | | r | 1 1 | e | 1 1 | s +1 1 * 1+ i | 1 | d | | u | | a | 1 | l | 1 | | | | | | | | 1 | | | | 1 | -1.4021 +---------------------------------+-------------------------+ -1.3677 predictor 1.0436 Scatterplot predictor V6 vs residual U1

0.6003 +---------------------------------+-------------------------+ | 1 | | | | | | 1 | | | | 1 | r | 1| e | | s | 1 | i | 1 | d |1 | u + 1 * 1 + a | 1 | l | 1 | | | | | | | | 1 1 | | | | 1 1 | -0.5131 +---------------------------------+-------------------------+ -1.3677 predictor 1.0436

Scatterplot predictor V6 vs residual U2

langer.soziologie.uni-halle.de · equations appear is arbitrary. the terms used in the level-1...

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